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EDUC 

LIBRA 




THE LIBRARY 

OF 

THE UNIVERSITY 
OF CALIFORNIA 

Education 

GIFT OF 

Mrs. T. M. Dunn 



N 



ON 



THE CONNECTION 



THE PHYSICAL SCIENCES, 



BY MARY SOMERVILLE. 






From tUa Seventh Loinioo Edition. 



TWO 

NEW YORK: 

HARPER & BROTHERS, PUBLISHERS, 

82 CLIFF STREET. 

1846. 



Education 
Add fii 

GIFT 



u 



PJIEFACE. 



THE progress of modern science, especially 
within the last few years, has been remarkable for 
a tendency to simplify the laws of nature, and to 
unite detached branches by general principles. In 
some cases identity has been proved where^ there 
appeared to be nothing in common, as in the 
electric and magnetic influences ; in others, as 
that of light and heat, such analogies have been 
pointed out as to justify the expectation that they 
will ultimately be referred to the same agent, and, 
in all there exists such a bond of union, that pro- 
ficiency cannot be attained in any one without a 
knowledge of others. 

Although well aware that a far more extensive 
illustration of these views might have been given, 
the Author hopes that enough has been done to 
show the Connection of the Physical Sciences. 

In order to keep pace with the progress of 
discovery in various branches of the Physical 
Sciences, this book has been carefully revised. 



076 



CONTENTS. 



INTRODUCTION . . .'," ' . ~ ' /. "7- " , . . Pag 1 

SECTION I. 

Attraction of a Sphere Form of Celestial'Bodies Terrestrial Gravitation 
retains the Moon in her Orbit The Heavenly Bodies move in Conic 
Sections Gravitation proportional to Mass Gravitation of the Particles 
of Matter Figure of the Planets How it affects the Motions of their 
' Satellites Rotation and Translation impressed by the same Impulse- 
Motion of the Sun and Solar System 4 

SECTION II. 

Elliptical Motion Mean and True Motion Equinoctial Ecliptic Equi- 
noxes Mean and True Longitude Equation of Center Inclination of 
the Orbits of Planets Celestial Latitude Nodes Elements of an Orbit 
Undisturbed or Elliptical Orbits Great Inclination of the Orbits of 
the new Planets Universal Gravitation the Cause of Perturbations in 
the Motions of the Heavenly Bodies Problem of the Three Bodies 
Stability of Solar System depends upon the Primitive Momentum of the 
Bodies 8 



SECTION in. 

Perturbations, Periodic and Circular Disturbing Action equivalent to 
three Partial Forces Tangential Force the Cause of the Periodic Ine- 
qualities in Longitude, and Secular Inequalities in the Form and Position 
of the Orbit in its own Plane Radial Force the Cause of Variations in 
the Planet's Distance from the Sun It combines with the Tangential 
Force to produce the Secular Variations in the Form and Position of the 
Orbit in its own Plane Perpendicular Force the Cause of Periodic Per- 
turbations in Latitude, and Secular Variations in the Position of the 
Orbit with regard to the Plane of the Ecliptic Mean Motion and Major 
Axis Invariable Stability of System Effects of a Resisting Medium 
Invariable Plane of the Solar System and of the Universe Great Ine- 
quality of Jupiter and Saturn 12 

SECTION IV. 

Theory of Jupiter's Satellites Effects of the Figure of Jupker upon his 
Satellites Position of their Orbits Singular Laws among the Motions 
of the first three Satellites Eclipses of the Satellites Velocity of Light 
Aberration Ethereal Medium Satellites of Saturn and Uranns 26 



VI CONTENTS. 

9 SECTION V. 

Lunar Theory Periodic Perturbations of the Moon Equation of Center 
Evection Variation Annual Equation Direct and Indirect Action of 
Planets The Moon's Action on the Earth disturbs her own Motion- 
Eccentricity and Inclination of Lunar Orbit Invariable Acceleration 
Secular Variation in Nodes and Perigee Motion of Nodes and Perigee 
inseparably connected with the Acceleration Nutation of Lunar Orbit 
Form and Internal Structure of the Earth determined from it Lunar, 
Solar, and Planetary Eclipses Occultations and Lunar Distances Mean 
Distance of the Sun from the Earth obtained from Lunar Theory Abso- 
lute Distances of the Planets, how found .... Page 33 

SECTION VI. 

Form of the Earth and Planets Figure of a Homogeneous Spheroid in 
Rotation Figure of a Spheroid of Variable Density Figure of the 
Earth, supposing it to be an Ellipsoid of Revolution Mensuration of a 
Degree of the Meridian Compression and Size of the Earth from 
Degrees of Meridian Figure of Earth from the Pendulum . 43 

SECTION VII. 

Parallax Lunar Parallax found from direct Observation Solar Parallax 
deduced from the Transit of Venus Distance of the Sun from the 
Earth Annual Parallax Distance of the Fixed Stars . . 51 



SECTION VIII. 

Masses of Planets that have no Satellites determined from their Perturba- 
tions Masses of the others obtained from the Motions of their Satellites 
Masses of the Sun, the Earth, of Jupiter, and of the Jovial System 
Mass of the Moon Real Diameters of Planets, how obtained Size of 
Sun Densities of the Heavenly Bodies Formation of Astronomical 
Tables Requisite Data and Means of obtaining them . . . 54 



SECTION IX. 

Rotation of the Sun and Planets Saturn's Rings Periods of the Rotation 
of the Moon and other Satellites equal to the Periods of their Revolu- 
tions Form of Lunar Spheroid Libration, Aspect, and Constitution of 
the Moon Rotation of Jupiter's Satellites GO 



SECTION X. 

Rotation of the Earth invariable Decrease in the Earth's Mean Tempera- 
ture Earth originally in a State of Fusion Length of Day constant 
Decrease of Temperature ascribed by Sir John Herschel to the Variation 
in the Eccentricity of the Terrestrial Orbit Difference in the Tempera- 
ture of the Two Hemispheres, erroneously ascribed to the Excess in the 
Length of Spring and Summer in the Southern Hemisphere ; attributed 
by Mr. Lyell to the Operation of existing Causes Three Principal Axes 
of Rotation Position of the Axis of Rotation on the Surface of the Earth 
invariable Ocean not sufficient to restore the Equilibrium of the Earth 
if deranged Its Density and Mean Depth Internal Structure of the 
Earth m 



CONTENTS. VJi 

SECTION XI. - 

Precession and Nutation Their Effects on the Apparent Places of the 
Fixed Stars Page 74 

SECTION XII. 

Mean and Apparent Sidereal Time Mean and Apparent Solar Time 
Equation of Time English and French Subdivisions of Time Leap 
Year Christian Era Equinoctial Time Remarkable Eras depending 
upon the Position of the Solar Perigee Inequality of the Lengths of 
the Seasons in the two Hemispheres Application of Astronomy to Chro- 
nology English and French Standards of Weights and Measures 77 

SECTION XIII. 

Tides Forces that produce them Three kinds of Oscillations in the Ocean 
The Semidiurnal Tides Equinoctial Tides Effects of the Declina- 
tion of the Sun and Moon Theory insufficient without Observation 
Direction of the Tidal Wave Height of Tides Mass of Moon obtained 
from her Action on the Tides Interference of Undulations Impossi- 
bility of a Universal Inundation Currents . . . . . 85 

SECTION XIV. 

Repulsive Force Interstices or Pores Elasticity Mossotti's Theory 
Gravitation brought under the same law with Molecular Attraction and 
Repulsion Gases reduced to Liquids by Pressure Intensity of the Co- 
hesive Force Effects of Gravitation Effects of Cohesion Minuteness 
of the ultimate Atoms of Matter Limited Height of the Atmosphere 
Theory of Definite Proportions and Relative Weight of Atoms Dr. Far- 
aday's Discoveries with regard to Affinity Composition of Water by a 
Plate of Platina Crystalization Cleavage Isomorphism Matter con- 
sists of Atoms of Definite Form Capillary Attraction . 96 

SECTION XV. 

Analysis of the Atmosphere Its Pressure Law of Decrease in Density 
Law of Decrease in Temperature Measurement of Heights by the 
Barometer Extent of the Atmosphere Barometrical Variations Oscil- 
lations Trade Winds Monsoons Rotation of Winds Laws of Hur- 
ricanes Water-Spouts Ill 

SECTION XVI. 

Sound Propagation of Sound illustrated by a Field of Standing Corn 
Nature of Waves Propagation of Sound through the Atmosphere 
Intensity Noises A Musical Sound Quality Pitch Extent ^of 
Human Hearing Velocity of Sound in Air, Water, and Solids Causes 
of the Obstruction of Sound Law of its Intensity Reflection of Sound 
Echoes Thunder Refraction of Sound Interference of Sounds 122 



SECTION XVII. 

Vibration of Musical Strings Harmonic Sounds Nodes Vibration of Air 
in Wind Instruments Vibration of Solids Vibrating Plates Bells- 
Harmony Sounding- Boards Forced Vibrations Resonance Speaking 
Machines . 134 



VI11 CONTENTS. 

SECTION XVIII. 

Refraction Astronomical Refraction and its Laws Formation of Tables of 
Refraction Terrestrial Refraction Its Quantity Instances of Extraor- 
dinary Refraction Reflection Instances of Extraordinary Reflection 
Loss of Light by the Absorbing" Power of the Atmosphere Apparent 
Magnitude of Sun and Moon in the Horizon . . . Page 147 

SECTION XIX. 

Constitution of Light according to Sir Isaac Newton Absorption of Light 
Colors of Bodies Constitution of Light according to Sir David Brew- 
ster New Colors in the Solar Spectrum Fraunhofer's Dark Lines 
Dispersion of Light The Achromatic Telescope Homogeneous Light 
Accidental and Complementary Colors M. Plateau's Experiments and 
Theory of Accidental Colors 153 

SECTION XX. 

Interference of Light Undulatory Theory of Light Propagation of Light 
Newton's Rings Measurement of the Length of the Waves of Light, 
and of the Frequency of the Vibrations of Ether for each Color New- 
ton's Scale of Colors Diffraction of Light Sir John HerschePs Theory 
of the Absorption of Light Refraction and Reflection of Light 161 

SECTION XXI. 

Polarization of Light Denned Polarization by Refraction Properties of 
the Tourmaline Double Refraction All doubly Refracted Light is 
Polarized Properties of Iceland Spar Tourmaline absorbs one of the 
two Refracted Rays Undulations of Natural Light Undulations ot 
Polarized Light The Optic Axes of Crystals M. Fresnel's Discoveries 
on the Rays passing along the Optic Axis Polarization by Reflection 172 

SECTION XXII. 

Phenomena exhibited by the passage of Polarized Light through Mica and 
Sulphate of Lime The Colored Images produced by Polarized Light 
passing through Crystals having one and two Optic Axes Circular 
Polarization Elliptical Polarization Discoveries of MM. Biot, Fresnel, 
and Professor Airy Colored Images produced by the Interference of 
Polarized Rays 180 

SECTION XXIII. 

Objections to the Undulatory Theory, from a Difference in the Action of 
Sound and Light under the same circumstances, removed The Disper- 
sion of Light according to the Undulatory Theory . . . 190 

SECTION XXIV. 

Chemical or Photographic Rays of the Solar Spectrum Messrs. Scheele, 
Ritter, a-nd Wollaston's Discoveries Mr. Wedgewood and Sir Humphry 
Davy's Photographic Pictures The Calotype The Daguerreotype 
The Chromatype The Cyanotype Sir John Herschel's Discoveries in 
the Photographic or Chemical Spectrum Mons. E. Becquerel's Discovery 
of Inactive Lines in the Chemical Spectrum . . . 193 



CONTENTS. ix 

SECTION XXV. 

Heat Calorific Rays of the Solar Spectrum Experiments of MM. De 
Laroche and Melloui on the Transmission of Heat The Point of greatest 
Heat in the Solar Spectrum varies with the Substance of the Prism 
Polarization of Heat Circular Polarization of Heat Transmission of the 
Chemical Rays Absorption of Heat Radiation of Heat Dew Hoar 
Frost Rain Hail Combustion Dilatation of Bodies by Heat Propa- 
gation of Heat Latent Heat Heat presumed to consist of the Undula- 
tions of an Elastic Medium Parathermic Rays Moser's Discoveries 

Page. 906 

SECTION XXVI. 

Atmosphere of the Planets and the Moon Constitution of the Sun Esti- 
mation of the Sun's Light His Influence on the different Planets 
Temperature of Space Internal Heat of the Earth Zone of Constant 
Temperature Heat increases with the Depth Heat in Mines and 
Wells Thermal .Springs Central Heat Volcanic Action The Heat 
above the Zone of Constant Temperature entirely from the Sun The 
Quantity of Heat annually received from the Sun Isogeothermal Lines 
Distribution of Heat on the Earth Climate Line of Perpetual Con- 
gelation Causes affecting Climate Isothermal Lines Excessive Cli- 
mates The same Quantity of Heat annually received and radiated by 
the Earth 238 

SECTION XXVII. 

Influence of Temperature on Vegetation Vegetation varies with the Lati- 
tude and Height above the Sea Geographical Distribution of Land 
Plants Distribution of Marine Plants Corallines, Shell-fish, Reptiles, 
Insects, Birds, and Quadrupeds Varieties of Mankind, yet Identity of 
Species 202 



SECTION XXVIIL 



Of ordinary Electricit 



iry Electricity, generally called Electricity of Tension Methods 
of exciting Bodies Transference Electrics and Non- Electrics Law of 
its Intensity Distribution Tension Electric Heat and Light Atmos- 
pheric Electricity Its Cause Electric Clouds Back Stroke Violent 
Effects of Lightning Its Velocity Phosphorescence Phosphorescent 
Action of Solar Spectrum Aurora 271 

SECTION XXIX. 

Voltaic Electricity The Voltaic Battery Intensity Quantity Compari- 
son of the Electricity of Tension with Electricity in Motion Luminous 
Effects Decomposition of Water Formation of Crystals by Voltaic 
Electricity Electrical Fish 290 

SECTION XXX. 

Terrestrial Magnetism Magnetic Poles Lines of equal and no Variation 
' The Dip The Magnetic Equator Magnetic Intensity Secular, peri- 
odic, and transitory Variations in the Magnetic Phenomena Origin of 
the Mariner's Compass Natural Magnets Artificial Magnets Polarity 
Induction Intensity Hypothesis of two Magnetic Fluids Distribu- 
tion of the Magnetic Fluid Analogy between Magnetism and Elec- 
tricity .300 



X CONTENTS. 

SECTION XXXI. 

Discovery of Electro-MagnetismDeflection of the Magnetic Needle by a 
Current of Electricity Direction of the Force Rotatory Motion by Elec- 
tricity Rotation of a Wire and a Magnet Rotation of a Magnet about 
its Axis Of Mercury and Water Electro-Magnetic Cylinder or Helix 
Suspension of a Needle in a Helix Electro-Magnetic Induction Tem- 
porary Magnets The Galvanometer . . . . . Page 314 

SECTION XXXII. 

Electro-DynamicsReciprocal Action of Electric Currents Identity of 
Electro-Dynamic Cylinders and Magnets Differences between the Ac- 
tion of Voltaic Electricity and Electricity of Tension Effects of a Voltaic 
Current Ampere's Theory . 319 

SECTION XXXIII. 

Magneto-Electricity Volta-Electric Induction Magneto-Electric Induc- 
tion Identity in the Action of Electricity and Magnetism Description 
of a Magneto-Electric Apparatus and its Effects Identity of Magnetism 
and Electricity . 322 

SECTION XXXIV. 

Electricity produced by Rotation Direction of the Currents Electricity 
from the Rotation of a Magnet M. Arago's Experiment explained 
Rotation of a Plate of Iron between the Poles of a Magnet Relation of 
Substances to Magnets of three kinds Thermo-Electricity . 325 

SECTION XXXV. 

The Action of Terrestrial Magnetism upon Electric Currents Induction 
of Electric Currents by Terrestrial Magnetism The Earth Magnetic by 
Induction Mr. Barlow's Experiment of an Artificial Sphere The Heat 
of the Sun the Probable Cause of Electric Currents in the Crust of the 
Earth ; and of the Variations in Terrestrial Magnetism Electricity of 
Metallic Veins Terrestrial Magnetism possibly owing to Rotation 
Magnetic Properties of the Celestial Bodies Identity of the Five Kinds 
of Electricity Connection between Light, Heat, and Electricity or Mag- 
netism 329 

SECTION XXXVI. 

Ethereal Medium Comets Do not disturb the Solar System Their 
Orbits and Disturbances M. Faye's Comet, probably the same- with 
Lexel's Periods of other three known Halley's Acceleration in the 
Mean Motions of Encke's and Biela's Comets The Shock of a Comet 
Disturbing Action of the Earth and Planets on Encke's and Biela's 
Comets Velocity of Comets The Great Comet of 1843 Physical Con- 
stitutionShine by borrowed Light Estimation of their Number . 337 

SECTION XXXVII. 

The Fixed Stars Their Numbers Estimation of their Distances and 
Magnitudes from their Light Stars that have vanished New Stars 
Double Stars Binary and Multiple Systems Their Orbits and Periods 
Orbitual and Parallactic Motions Colors Proper Motions General 



CONTENTS. XI 

Motions of all the Stars Clusters Nebula Their Number and Forms 
Double and Stellar Nebulae Nebulous Stars Planetary Nebulse 
Constitution of the Nebula?, and Forces which maintain them Distribu- 
tion Meteorites Shooting Stars Page 361 

SECTION XXXVIII. 

Diffusion of Matter through Space Gravitation Its Velocity Simplicity 
of its Laws Gravitation independent of the Magnitude and Distances of 
the Bodies Not impeded by the Intervention of any Substance Its 
Intensity invariable General Laws Recapitulation and Conclusion 386 

NOTES . 391 

INDEX 445 






CONNECTION OF PHYSICAL SCIENCES. 



INTRODUCTION. 

SCIENCE, regarded as the pursuit of truth, must ever 
afford occupation of consummate interest, and subject of 
elevated meditation. The contemplation of the works 
of creation elevates the mind to the admiration of what- 
ever is great and noble ; accomplishing the object of all 
study, which, in the eloquent language of Sir James 
Mackintosh, "is to inspire the love of truth, of wisdom, 
of beauty especially of goodness, the highest beauty 
and of that supreme and eternal Mind, which con- 
tains all truth and wisdom, all beauty and goodness. 
By the love or delightful contemplation and pursuit of 
these transcendent aims, for their own sake only, the 
mind of man is raised from low and perishable objects, 
and prepared for those high destinies which are ap- 
pointed for all those who are capable of them." 

Astronomy affords the most extensive example of the 
connection of the physical sciences. In it are combined 
the sciences of number and quantity, of rest and mo- 
tion. In it we perceive the operation of a force which 
is mixed up with everything that exists in the heavens 
or on earth; which pervades every atom, rules the 
motions of animate and inanimate beings, and is as sen- 
sible in the descent of a rain-drop as in the falls of 
Niagara; in the weight of the air, as in the periods of 
the moon. Gravitation not only binds satellites to their 
planet, and planets to the sun, but it connects sun with 
sun throughout the wide extent of creation, and is the 
cause of the disturbances, as well as of the order of 
nature : since every tremor it excites in any one planet 
is immediately transmitted to the farthest limits of the 
system, in oscillations, which correspond in their periods 
with the cause producing them, like sympathetic notes 
in music, or vibrations from the deep tones of an organ. 

The heavens afford the most sublime subject of study 
which can be derived from science. The magnitude 
1 A 



2 INTRODUCTION. 

and splendor of the objects, the inconceivable rapidity 
with which they move, and the enormous distances 
between them, impress the mind with some notion of 
the energy that maintains them in their motions, with a 
durability to which we can see no limit. Equally con- 
spicuous is the goodness of the great First Cause, in 
having endowed man with faculties, by which he can 
not only appreciate the magnificence of His works, but 
trace, with precision, the operation of His laws, use the 
globe he inhabits as a base wherewith to measure the 
magnitude and distance of the sun and planets, and 
make the diameter (Note 1) of the earth's orbit the 
first step of a scale by which he may ascend to the 
starry firmament. Such pursuits, while they ennoble 
the mind, at the same time inculcate humility, by show- 
ing that there is a barrier which no energy, mental or 
physical, can ever enable us to pass : that, however 
profoundly we may penetrate the depths of space, 
there still remain innumerable systems, compared with 
which, those apparently so vast must dwindle into in- 
significance, or even become invisible ; and that not only 
man, but the globe he inhabits nay, the whole system 
of which it forms so small a part might be annihilated, 
and its extinction be unperceived in the immensity of 
creation. 

A complete acquaintance with physical astronomy 
can be attained by those only who are well versed in 
the higher branches of mathematical and mechanical 
science (N. 2), and they alone can appreciate the ex- 
treme beauty of the results, and of the means by which 
these results are obtained. It is nevertheless true, that 
a sufficient skill in analysis (N. 3) to follow the general 
outline to see the mutual dependence of the different 
parts of the system, and to comprehend by what means 
the most extraordinary conclusions have been arrived 
at, is within the reach of many who shrink from the 
task, appalled by difficulties, not more formidable than 
those incident to the study of the elements of every 
branch of knowledge. There is a wide distinction be- 
tween the degree of mathematical acquirement neces- 
sary for making discoveries, and that which is requisite 
for understanding what others have done. 



INTRODUCTION. 3 

Our knowledge of external objects is founded upon 
experience, which furnishes facts ; the comparison of 
these facts establishes relations, from which the belief 
that like causes will produce like effects, leads to gen- 
eral laws. Thus, experience teaches that bodies fall at 
the surface of the earth with an accelerated velocity, 
and with a force proportional to their masses. By com- 
parison, Newton proved that the force which occasions 
the fall of bodies at the earth's surface is identical with 
that which retains the moon in her orbit; and he con- 
cluded, that as the moon is kept in her orbit by the 
attraction of the earth, so the planets might.be retained 
in their orbits by the attraction of the sun. By such 
steps he was led to the discovery of one of those powers, 
with which the Creator has ordained, that matter should 
reciprocally act upon matter. 

Physical astronomy is the science which compares 
and identifies the laws of motion observed on earth, 
with the motions that take place in the heavens ; and 
which traces, by an uninterrupted chain of deduction 
from the great principle that governs the universe, the 
revolutions and rotations of the planets, and the oscilla- 
tions (N. 4) of the fluids at their surfaces; and which 
estimates the changes the system has hitherto under- 
gone, or may hereafter experience changes which 
require millions of years for their accomplishment. 

The accumulated efforts of astronomers, from the 
earliest dawn of civilization, have been necessary to 
establish the mechanical theoiy of astronomy. The 
courses of the planets have been observed for ages, with 
a degree of perseverance that is astonishing, if we con- 
sider the imperfection and even the want of instruments. 
The real motions of the earth have been separated 
from the apparent motions of the planets ; the laws of 
the planetary revolutions have been discovered ; and 
the discovery of these laws has led to the knowledge of 
the gravitation (N. 5) of matter. On the other hand, 
descending from the principle of gravitation, every mo- 
tion in the solar system has been so completely explained, 
that the laws of any astronomical phenomena that may 
hereafter occur, are already determined. 



ATTRACTION OP A SPHERE. SKCT. I. 



SECTION I. 

Attraction of a Sphere Form of Celestial Bodies Terrestrial Gravitation 
retains the Moon in her Orbit The Heavenly Bodies move in Conic 
Sections Gravitation proportional to Mass Gravitation of the Particles 
of Matter Figure of the Planets How it affects the Motions of their 
Satellites Rotation and Translation impressed by the same Impulse 
Motion of the Sun and Solar System. 

IT has been proved by Newton, that a particle of mat- 
ter (N. G) placed without the surface of a hollow sphere 
(N. 7), is attracted by it in the same manner as if the 
mass of the hollow sphere, or the whole matter it con- 
tains, were collected into one dense particle in its center. 
The same is therefore true of a solid sphere, which may 
be supposed to consist of an infinite number of concentric 
hollow spheres (N. 8). This, however, is not the case 
with a spheroid (N. 9) ; but the celestial bodies are so 
nearly spherical, and at such remote distances from one 
another, that they attract and are attracted as if each 
were condensed into a single particle situate in its center 
of gravity (N. 10) a circumstance which greatly facili- 
tates the investigation of their motions. 

Newton has shown that the force which retains the 
moon in her orbit, is the same with that which causes 
heavy substances to fall at the surface of the earth. If 
the earth were a sphere, and at rest, a body would be 
equally attracted, that is, it would have the same weight 
at every point of its surface, because the surface of a 
sphere is everywhere equally distant from its center. 
But as our planet is flattened at the poles (N. 11), and 
bulges at the equator, the weight of the same body 
gradually decreases from the poles, where it is greatest, 
to the equator, where it is least. There is, however, a 
certain mean (N. 12) latitude (N. 13), or pait of the earth 
intermediate between the pole and the equator, where 
the attraction of the earth on bodies at its surface is the 
same as if it were a sphere ; and experience shows that 
bodies there fall through 16-0697 feet in a second. The 
mean distance (N. 14) of the moon from the earth is 
about sixty times the mean radius (N. 15) of the earth. 
When the number 16-0697 is diminished in the ratio 



SECT. I. UNIVERSAL GRAVITATION. 5 

(N. 16) of 1 to 3600, which is the square of the moon's 
distance (N. 17) from the earth's center, estimated in 
terrestrial radii, it is found to be exactly the space the 
noon would fall through in the first second of her de- 
scent to the earth, were she not prevented by the cen- 
trifugal force (N. 18) arising from the velocity with 
which she moves in her orbit. The moon is thus re- 
tained in her orbit by a force having the same origin, 
and regulated by the same law, with that which causes 
a stone to fall at the earth's surface. The earth may 
therefore be regarded as the center of a force which 
extends to the moon ; and, as experience shows that the 
action and reaction of matter are equal and contrary 
(N. 19), the moon must attract the earth with an equal 
and contrary force. 

Newton also ascertained that a body projected (N. 20) 
in space (N. 21), will move in a conic section (N. 22), if 
attracted by a force proceeding from a fixed point, with an 
intensity inversely as the square of the distance (N. 23) ; 
but that any deviation from that Iftw will cause it to move 
in a curve of a different nature. Kepler found, by direct 
observation, that the planets descripe ellipses (N. 24), or 
oval paths, round the sun. Later observations show 
that comets also move in conic sections. It consequently 
follows, that the sun attracts all the planets and comets 
inversely as the square of their distance? from his cen- 
ter ; the sun, therefore, is the center of a force extend- 
ing indefinitely in space, and including all the bodies of 
the system in its action. 

Kepler also deduced from observation, that the squares 
of the periodic times (N. 25) of the planets, or the times 
of their revolutions round the sun, are proportional to 
the cubes of their mean distances from his center 
(N. 26). Hence the intensity of gravitation of all the 
bodies toward the sun is the same at equal distances. 
Consequently, gravitation is proportional to the masses 
(N. 27); for, if the planets and comets were at equal 
distances from the sun, and left to the effects of gravity, 
they would arrive at his surface at the same time 
(N. 28). The satellites also gravitate to their primaries 
(N. 29) according to the same law that their primaries 
do to the sun. Thus, by the law of action and reaction, 
Afl 



6 FORM OF PLANETS. SBCT. I. 

each body is itself the center of an attractive force ex- 
tending indefinitely in space, causing all the mutual dis- 
turbances which render the celestial motions so compli- 
cated, and their investigation so difficult. 

The gravitation of matter directed to a center, and 
attracting directly as the mass, and inversely as the 
square of the distance, does not belong to it when con- 
sidered in mass only ; particle acts on particle according 
to the same law when at sensible distances from each 
other. If the sun acted on the center of the earth, with- 
out attracting each of its particles, the tides would be 
very much greater than they now are, and would also, 
in other respects, be very different. The gravitation of 
the earth to the sun results from the gravitation of all its 
particles, which, in their turn, attract the sun in the ra- 
tio of their respective masses. There is a reciprocal 
action, likewise, between the earth and every particle 
at its surface. The earth and a feather mutually attract 
each other in the proportion of the mass of the earth to 
the mass of the feather. Were this not the case, and 
were any portion of the earth, however small, to attract 
another portion, and not be itself attracted, the center of 
gravity of the earth would be moved in space by this 
action, which is impossible. 

The forms of the planets result from the reciprocal 
attraction of their component particles. A detached fluid 
mass, if at rest, would assume the form of a sphere, 
from the reciprocal attraction of its particles. But if the 
mass revolve about an axis, it becomes flattened at the 
poles, and bulges at the equator (N. 11), in consequence 
of the centrifugal force arising from the velocity of rota- 
tion (N. 30) ; for the centrifugal force diminishes the 
gravity of the particles at the equator, and equilibrium 
can only exist where these two forces are balanced by 
an increase of gravity. Therefore, as the attractive force 
is the same on all particles at equal distances from the 
center of a sphere, the equatorial particles would recede 
from the center, till their increase in number balance 
the centrifugal force by their attraction. Consequently, 
the sphere would become an oblate, or flattened sphe- 
roid ; and a fluid partially or entirely covering a solid, as 
the ocean and atmosphere cover the earth, must assume 



SECT. I. ROTATION AND TRANSLATION. 7 

that form in order to remain in equilibrio. The surface 
of the sea is therefore spheroidal, and the surface of the 
earth only deviates from that figure where it rises above 
or sinks below the level of the sea. But the deviation is 
so small, that it is unimportant when compared with the 
magnitude of the earth ; for the mighty chain of the 
Andes, and the yet more lofty Himalaya, bear about the 
same proportion to the earth that a grain of sand does to 
a globe three feet in diameter. Such is the form of the 
earth and planets. The compression (N. 31) or flatten- 
ing at their poles is, however, so small, that even Jupiter, 
whose rotation is the most rapid, and therefore the most 
elliptical of the planets, may, from his great distance, be 
regarded as spherical. Although the planets attract 
each other as if they were spheres, on account of their 
distances, yet the satellites (N. 32) are near enough to 
be sensibly affected in their motions by the forms of 
their primaries. The moon, for example, is so near 
the earth, that the reciprocal attraction between each of 
her particles, and each of the particles in the prominent 
mass at the terrestrial equator, occasions considerable 
disturbances in the motions of both bodies ; for the ac- 
tion of the moon on the matter at the earth's equator, 
produces a nutation (N. 33) in the axis (N. 34) of rotation, 
and the reaction of that matter on the moon is the cause 
of a corresponding nutation in the lunar orbit (N. 35). 

If a sphere at rest in space receive an impulse passing 
through its center of gravity, all its parts will move with 
an equal velocity in a straight line ; but if the impulse 
does not pass though the center of gravity, its particles, 
having unequal velocities, will have a rotatory or revolv- 
ing motion, at the same time that it is translated (N. 36) 
in space. These motions are independent of one an- 
other ; so that a contrary impulse, passing through its 
center of gravity, will impede its progress, without in- 
terfering with its rotation. As the sun rotates about an 
axis, it seems probable, if an impulse in a contrary direc- 
tion has not been given to his center of gravity, that he 
moves in space, accompanied by all those bodies which 
compose the solar system a circumstance which would 
in no way interfere with their relative motions ; for, in 
consequence of the principle, that force is proportional 



8 ELLIPTICAL MOTION. SECT. II. 

to velocity (N. 37), the reciprocal Attractions of a system 
remain the same, whether its center of gravity be at 
rest, or moving uniformly in space. It is computed that, 
had the earth received its motion from a single impulse, 
that impulse must have passed through a point about 
twenty-five miles from its center. 

Since the motions of rotation and translation of the 
planets are independent of each other, though probably 
communicated by the same impulse, they form separate 
subjects of investigation. 



SECTION II. 

Elliptical Motion Mean and True Motion Equinoctial Ecliptic Equi- 
noxes Mean and True Longitude Equation of Center Inclination of 
the Orbits of Planets Celestial Latitude Nodes Elements of an Orbit 
Undisturbed or Elliptical Orbits Great Inclination of the Orbits of 
the new Planets Universal Gravitation the Cause of Perturbations in 
the Motions of the Heavenly Bodies Problem of the Three Bodies 
Stability of Solar System depends upon the Primitive Momentum of the 
Bodies. 

A PLANET moves in its elliptical orbit with a velocity 
varying every instant, in consequence of two forces, one 
tending to the center of the sun, and the other in the 
direction of a tangent (N. 38) to its orbit, arising from 
the primitive impulse, given at the time when it was 
launched into space. Should the force in the tangent 
cease, the planet would fall to the sun by its gravity. 
Were the sun not to attract it, the planet would fly off 
in the tangent. Thus, when the planet is at the point 
of its orbit farthest from the sun, his action overcomes 
the planet's velocity, and brings it toward him with 
such an accelerated motion, that at last it overcomes the 
sun's attraction ; and shooting past him, gradually de- 
creases in velocity, until it arrives at the most distant 
point, where the sun's attraction again prevails (N. 39). 
In this motion the radii vector es (N. 40), or imaginary 
lines joining the centers of the sun and the planets, pass 
over equal areas or spaces in equal times (N. 41). 

The mean distance of a planet from the sun is equal 
to half the major axis (N. 42) of its orbit : if, therefore, 
the planet described a circle (N. 43) round the sun at 



SCT. IL ELLIPTICAL MOTION. 9 

its mean distance, the motion would be uniform, and 
the periodic time unaltered, because the planet would 
arrive at the extremities of the major axis at the same 
instant, and would have the same velocity, whether it 
moved in the circular or elliptical orbit, since the curves 
coincide in these points. But, in every other part, the 
elliptical or true motion (N. 44) would either be faster 
or slower than the circular or mean motion (N. 45). As 
it is necessary to have some fixed point in the heavens 
from whence to estimate these motions, the vernal equi- 
nox (N. 46) at a given epoch has been chosen. The 
equinoctial, which is a great circle traced in the starry 
heavens by the imaginary extension of the plane of the 
terrestrial equator, is intersected by the ecliptic, or ap- 
parent path of the sun, in two. points diametrically oppo- 
site to one another, called the vernal and autumnal 
equinoxes. The vernal equinox is the point through 
which the sun passes, in going from the southern to the 
northern hemisphere ; and the autumnal, that in which 
he crosses from the northern to the southern. The 
mean or circular motion of a body, estimated from the 
vernal equinox, is its mean longitude ; and its elliptical, 
or true motion, reckoned from that point, is its true lon- 
gitude (N. 47) : both being estimated from west to east, 
the direction in which the bodies move. The difference 
between the two is called the equation of the center 
(N. 48) ; which consequently vanishes at the apsides 
(N. 49), or extremities of the major axis, and is at its 
maximum ninety degrees (N. 50) distant from these 
points, or in quadratures (N. 51), where it measures 
the eccentricity (N. 52) of the orbit ; so that the place 
of a planet in its elliptical orbit is obtained, by adding or 
subtracting the equation of the center to or from its 
mean longitude. 

The orbits of the planets have a very small obliquity 
or inclination (N. 53) to the plane of the ecliptic in which 
the earth moves ; and on that account, astronomers refer 
their motions to this plane at a given epoch as a known 
and fixed position. The angular distance of a planet 
from the plane of the ecliptic is its latitude (N. 54) ; 
which is south or north, according as the planet is south 
or north of that plane. When the planet 10 in the plane 



10 ORBITS OF THE PLANETS. SECT. II. 

of the ecliptic, its latitude is zero : it is then said to be 
in its nodes (N. 55). The ascending node is that point 
in the ecliptic, through which the planet passes, in going 
from the southern to the northern hemisphere. The 
descending node is a corresponding point in the plane of 
the ecliptic diametrically opposite to the other, through 
which the planet descends in going from the northern 
to the southern hemisphere. The longitude and lati- 
tude of a planet cannot be obtained by direct observa- 
tion, but are deduced from observations made at the 
surface of the earth, by a very simple computation. 
These two quantities, however, will not give the place 
of a planet in space. Its distance from the sun (N. 56) 
must also be known ; and, for the complete determina- 
tion of its elliptical motion, the nature and position of its 
orbit must be ascertained by observation. This depends 
upon seven quantities, called the elements of the ortyt 
(N. 57). These are, the length of the major axis, and 
the eccentricity, which determine the form of the orbit: 
the longitude of the planet when at its least distance 
from the sun, called the longitude of the perihelion ; the 
inclination of the orbit to the plane of the ecliptic, and 
the longitude of its ascending node ; these give the po- 
sition of the orbit in space ; but the periodic time, and 
the longitude of the planet at a given instant, called the 
longitude of the epoch, are necessary for finding the 
place of the body in its orbit at all times. A perfect 
knowledge of these seven elements is requisite, for as- 
certaining all the circumstances of undisturbed elliptical 
motion. By such means it is found, that the paths of 
the planets, when their mutual disturbances are omitted, 
are ellipses nearly approaching to circles, whose planes, 
slightly inclined to the ecliptic, cut it in straight lines, 
passing through the center of the sun (N. 58). The 
orbits of the recently discovered planets deviate more 
from the ecliptic than those of the ancient planets ; that 
of Pallas, for instance, has an inclination of 34 37' 50-2" 
to it ; on which account it is more difficult to determine 
their motions. 

Were the planets attracted by the sun only, they 
would always move in ellipses, invariable in form and 
position ; and because his action is proportional to his 



S*CT. II. PROBLEM OF THE THREE BODIES. 11 

mass, which is much larger than that of all the planets 
put together, the elliptical is the nearest approximation 
to their true motions. The true motions of the planets 
are extremely complicated, in consequence of their 
mutual attraction; so that they do not move in any 
known or symmetrical curve, but in paths now ap- 
proaching to, now receding from, the elliptical form ; 
and their radii vectores do not describe areas or spaces 
exactly proportional to the time, so that the areas be- 
come a test of disturbing forces. 

To determine the motion of each body, when dis- 
turbed by all the rest, is beyond the power of analysis. 
It is therefore necessary to estimate the disturbing ac- 
tion of one planet at a time, whence the celebrated 
problem of the three bodies, originally applied to the 
moon, the earth, and the sun ; namely, the masses 
being given of three bodies projected from three given 
points, with velocities given both in quantity and direc- 
tion ; and, supposing the bodies to gravitate to one an- 
other with forces that are directly as their masses, and 
Diversely as the squares of the distances, to find the 
lines described by these bodies, and their positions at 
any given instant : or, in other words, to determine the 
path of a celestial body when attracted by a second body, 
and disturbed in its motion round the second body by a 
third a problem equally applicable to planets, satellites, 
and comets. 

By this problem the motions of translation of the 
celestial bodies are determined. It is an extremely 
difficult one, and would be infinitely more so, if the dis- 
turbing action were not very small when compared with 
the central force ; that is, if the action of the planets on 
one another were not veiy small when compared with 
that of the sun. As the disturbing influence of each 
body may be found separately, it is assumed that the 
action of the whole system, in disturbing any one planet, 
is equal to the sum of all the particular disturbances it 
experiences, on the general mechanical principle, that 
the sum of any number of small oscillations is nearly 
equal to their simultaneous and joint effect. 

On account of the reciprocal action of matter, the 
stability of the system depends upon the intensity of the 



12 STABILITY OF SYSTEM. SECT. III. 

primitive momentum (N. 59) of the planets, and the 
ratio of their masses to that of the sun ; for the nature 
of the conic sections in which the celestial bodies move, 
depends upon the velocity with which they were first 
propelled in space. Had that velocity been such as to 
make the planets move in orbits of unstable equilibrium 
(N. 60), their mutual attractions might have changed 
them into parabolas, or even hyperbolas (N. 22) ; so 
that the earth and planets might, ages ago, have been 
sweeping far from our sun through the abyss of space. 
But as the orbits differ very little from circles, the mo- 
mentum of the planet, when projected, must have been 
exactly sufficient to insure the permanency and stability 
of the system. Besides, the mass of the sun is vastly 
greater than that of any planet ; and as their inequali- 
ties bear the same ratio to their elliptical motions, that 
their masses do to that of the sun, their mutual- disturb- 
ances only increase or diminish the eccentricities of their 
orbits, by very minute quantities ; consequently the mag- 
nitude of the sun's mass is the principal cause of the 
stability of the system. There is not in the physical 
world a more splendid example of the adaptation of 
means to the accomplishment of an end, than is exhib- 
ited in the nice adjustment of these forces, at once the 
cause of the variety and of the order of Nature. 



SECTION III. 

Perturbations, Periodic and Circular Disturbing Action equivalent to 
three Partial Forces Tangential Force the Cause of the Periodic Ine 
qualities in Longitude, and Secular Inequalities in the Form and Position 
of the Orbit in its own Plane Radial Force the Cause of Variations in 
the Planet's Distance from the Sun It combines with the Tangential 
Force to produce the Secular Variations in the Form and Position of the 
Orbit in its own Plane Perpendicular Force the Cause of Periodic Per- 
turbations in Latitude, and Secular Variations in the Position of the 
Orbit with regard to the Plane of the Ecliptic Mean Motion and Major 
Axis Invariable Stability of System Effects of a Resisting Medium 
Invariable Plane of the Solar System and of the Universe Great Ine- 
quality of Jupiter and Saturn. 

THE planets are subject to disturbances of two kinds, 
both resulting from the constant operation of their recip- 
rocal attraction : one kind, depending upon their posi- 



SECT. III. PERTURBATIONS. 13 

tions with regard to each other, begins from zero, in- 
creases to a maximum, decreases, and becomes zero 
again, when the planets return to the same relative 
positions. In consequence of these, the disturbed planet 
is sometimes drawn away from the sun, sometimes 
brought nearer to him : sometimes it is accelerated in 
its motion, and sometimes retarded. At one time it is 
drawn above the plane of its orbit, at another time below 
it, according to the position of the disturbing body. All 
such changes, being accomplished in short periods, some 
in a few months, others in years, or in hundreds of 
years, are denominated periodic inequalities. The in- 
equalities of the other kind, though occasioned likewise 
by the disturbing energy of the planets, are entirely in- 
dependent of their relative positions. They depend 
upon the relative positions of the orbits alone, whose 
forms and places in space are altered by very minute 
quantities, in immense periods of time, and are, there- 
fore, called secular inequalities. 

The periodical perturbations are compensated, when 
the bodies return to the same relative positions with 
regard to one another and to the sun : the secular ine- 
qualities are compensated, when the orbits return to 
the same positions relatively to one another, and to the 
plane of the ecliptic. 

Planetary motion, including both these kinds of dis- 
turbance, may be represented by a body revolving in an 
ellipse, and making small and transient deviations, now 
on one side of its path, and now on the other, while the 
ellipse itself is slowly, but perpetually, changing both in 
form and position. 

The periodic inequalities are merely transient devi- 
ations of a planet from its path, the most remarkable of 
which only lasts about 918 years; but, in consequence 
of the secular disturbances, the apsides, or extremities 
of the major axes of all the orbits, have a direct but 
variable motion in space, excepting those of the orbit of 
Venus, which are retrograde (N. 61), and the lines of 
the nodes move with a variable velocity in a contrary 
direction. Besides these, the inclination and eccen- 
tricity of every orbit are in a state of perpetual- but slow 
change. These effects result from the disturbing action 
B 



14 D1STUKBING FORCES. SJBCT. III. 

of all the planets on each. But as it is only necessary 
to estimate the disturbing influence of one body at a 
time, what follows may convey some idea of the manner 
in which one planet disturbs the elliptical motion of 
another. 

Suppose two planets moving in ellipses round the sun ; 
if one of them attracted the other and the sun with 
equal intensity, and in parallel directions (N. 62), it 
would have no effect in disturbing the elliptical motion. 
The inequality of this attraction is the sole cause of 
perturbation, and the difference between the disturbing 
planet's action on the sun and on the disturbed planet 
constitutes the disturbing force, which consequently 
varies in intensity and direction with every change in 
the relative positions of the three bodies. Although 
both the sun and planet are under the influence of the 
disturbing force, the motion of the disturbed planet is 
referred to the center of the sun as a fixed point, for 
convenience. The whole force (N. 63) which disturbs 
a planet is equivalent to three partial forces. One of 
these acts on the disturbed planet, in the direction of a 
tangent to its orbit, and is called the tangential force : it 
occasions secular inequalities in the form and position of 
the orbit in its own plane, and is the sole cause of the 
periodical perturbations in the planet's longitude. An- 
other acts upon the same body in the direction of its 
radius vector, that is, in the line joining the centers of 
the sun and planet, and is called the radial force : it 
produces periodical changes in the distance of the planet 
from the sun, and affects the form and position of the 
orbit in its own plane. The third, which may be called 
the perpendicular force, acts at right angles to the plane 
of the orbit, occasions the periodic inequalities in the 
planet's latitude, and affects the position of the orbit 
with regard to the plane of the ecliptic. 

It has been observed, that the radius vector of a 
planet moving in a perfectly elliptical orbit, passes over 
equal spaces or areas in equal times; a circumstance 
which is independent of the law of the force, and would 
be the same whether it varied /inversely as the square 
of the distance, or not, provided only that it be directed 
to the center of the sun. Hence the tangential force. 



SICT. III. MOTION OF THE APSIDES. 15 

not being directed to the center, occasioas an unequable 
description of areas, or, what is the same thing, it dis- 
turbs the motion of the planet in longitude. The tan- 
gential force sometimes accelerates the planet's motion, 
sometimes retards it, and occasionally has no effect at all. 
Were the orbits of both planets circular, a complete 
compensation would take place at each revolution of the 
two planets, because the arcs in which the accelerations 
and retardations take place, would be symmetrical on 
each side of the disturbing force. For it is clear, that 
if the motion be accelerated through a certain space, and 
then retarded through as much, the motion at the end 
of the time will be the same as if no change had taken 
place. But, as the orbits of the planets are ellipses, this 
symmetry does not hold ; for, as the planet moves un- 
equably in its orbit, it is in some positions more directly, 
and for a longer time, under the influence of the dis- 
turbing force than in others. And although multitudes 
of variations do compensate each other in short periods, 
there are others, depending on peculiar relations among 
the periodic times of- the planets, which do not compen- 
sate each other till after one, or even till after many 
revolutions of both bodies. A periodical inequality of 
this kind in the motions of Jupiter and Saturn, has a 
period of no less than 918 years. 

The radial force, or that part of the disturbing force 
which acts in the direction of the line joining the centers 
of the sun and disturbed planet, has no effect on the 
areas, but is the cause of periodical changes of small 
extent in the distance of the planet from the sun. It 
has already been shown, that the force producing per- 
fectly elliptical motion varies inversely as the square of 
the distance, and that a force following any other law 
would cause the body to move in a curve of a very dif- 
ferent kind. Now, the radial disturbing force varies 
directly as the distance ; and, as it sometimes combines 
with and increases the intensity of the sun's attraction 
for the disturbed body, and at other times opposes and 
consequently diminishes it, in both cases it causes the 
sun's attraction to deviate from the exact law of gravity, 
and the whole action of this compound central force on 
the disturbed body is either greater or less than what is 



16 MOTION OF THE APSIDES. SKCT. 111. 

requisite for perfectly elliptical motion. When greater, 
the curvature of the disturbed planet's path on leaving 
its perihelion (N. 64), or point nearest the sun, is 
greater than it would be in the ellipse, which brings the 
planet to its aphelion (N. 65), or point farthest from the 
sun, before it has passed through 180, as it would do 
if undisturbed. So that in this case the apsides, or ex- 
tremities of the major axis, advance in space. When 
the central force is less than the law of gravity requires, 
the curvature of the planet's path is less than the cur- 
vature of the ellipse. So that the planet, on leaving its 
perihelion, would pass through more than 180 before 
arriving at its aphelion, which causes the apsides to re- 
cede in space (N. 66). Cases both of advance and re- 
cess occur during a revolution of the two planets ; but 
those in which the apsides advance, preponderate. 
This, however, is not the full amount of the motion of 
the apsides ; part arises also from the tangential force 
(N. 63), which alternately accelerates and retards the 
velocity of the disturbed planet. An increase in the 
planet's tangential velocity diminishes the curvature of 
its orbit, and is equivalent to a decrease of central force. 
On the contrary, a decrease of the tangential velocity, 
which increases the curvature of the orbit, is equivalent 
to an increase of central force. These fluctuations, 
owing to the tangential force, occasion an alternate re- 
cess and advance of the apsides, after the manner 
already explained (N. 66). An uncompensated portion 
of the direct motion arising from this cause, conspires 
with that already impressed by the radial force, and in 
some cases even nearly doubles the direct motion of 
these points. The motion of the apsides may be repre- 
sented, by supposing a planet to move in an ellipse, 
while the ellipse itself is slowly revolving about the sun 
in the same plane (N. 67). This motion of the major 
axis, which is direct in all the orbits except that of the 
planet Venus, is irregular, and so slow, that it requires 
more than 109,830 years for the major axis of the 
earth's orbit to accomplish a sidereal revolution (N. 68), 
that is, to return to the same stars; and 20,984 years 
to complete its tropical revolution (N. 69), or to return 
to the same equinox. The difference between these 



SBCT. III. VARIATION LN THE ECCENTRICITY. 17 

two periods arises from a retrograde motion in the 
equinoctial point, which meets the advancing axis be- 
fore it has completed its revolution with regard to the 
stars. The major axis of Jupiter's orbit requires no 
less than 200,610 years to perform its sidereal revolution, 
and 22,743 years to accomplish its tropical revolution 
from the disturbing action of Saturn alone. 

A variation in the eccentricity of the disturbed planet's 
orbit, is an immediate consequence of the deviation from 
elliptical curvature, caused by the action of the dis- 
turbing force. When the path of the body, in pro- 
ceeding from its perihelion to its aphelion, is more curved 
than it ought to be from the effect of the disturbing forces, 
it falls within the elliptical orbit, the eccentricity is di- 
minished, and the orbit becomes more nearly circular ; 
when that curvature is less than it ought to be, the path 
of the planet falls without its elliptical orbit (N. 66), and 
the eccentricity is increased : during these changes, the 
length of the major axis is not altered, the orbit only 
bulges out, or becomes more flat (N. 70). Thus the 
variation in the eccentricity arises from the same cause 
that occasions the motion of the apsides (N. 67). There 
is an inseparable connection between these two ele- 
ments ; they vary simultaneously, and have the same 
period ; so that while the major axis revolves in an im- 
mense period of time, the eccentricity increases and 
decreases by very small quantities, and at length returns 
to its original magnitude at each revolution of the ap- 
sides. The terrestrial eccentricity is decreasing at the 
rate of about 40 miles annually ; and, if it were to de- 
crease equably, it would be 39,861 years before the 
earth's orbit became a circle. The mutual action of 
Jupiter and Saturn occasions variations in the eccentri- 
city of both orbits, the greatest eccentricity of Jupiter's 
orbit corresponding to the least of Saturn's. The 
period in which these vicissitudes are accomplished is 
70,414 years, estimating the action of these two planets 
alone : but if the action of all the planets were estimated, 
the cycle would extend to millions of years. 

That part of the disturbing force is now to be con- 
sidered which acts perpendicularly to the plane of the 
orbit, causing periodic perturbations in latitude, secular 
2 B2 



18 VARIATION IN THE INCLINATION. SECT. III. 

variations in the inclination of the oibit, and a retrograde 
motion to its nodes on the true plane of the ecliptic 
(N. 71). This force tends to pull the disturbed body 
above, or push (N. 72) it below, the plane of its orb.t, 
according to the relative pos.tions of the two planets with 
regard to the sun, considered to be fixed. By this 
action, it sometimes makes the plane of the orbit of the 
disturbed body tend to coincide with the plane of the 
ecliptic, and sometimes increases its inclination to that 
plane. In consequence of which, its nodes alternately 
recede or advance on the ecliptic (N. 73). When the 
disturbing planet is in the line of the disturbed planet's 
nodes (N. 74), it neither affects these points, the latitude, 
nor the inclination, because both planets are then in the 
same plane. When it is at right angles to the line of 
the nodes, and the orbit symmetrical on each side of the 
disturbing force, the average motion of these points, 
after a revolution of the disturbed body, is retrograde, 
and comparatively rapid ; but when the disturbing planet 
is so situated that the orbit of the disturbed planet is not 
symmetrical on each side of the disturbing force, which 
is most frequently the case, every possible variety of 
action takes place. Consequently, the nodes are per- 
petually advancing or receding with unequal velocity ; 
but, as a compensation is not effected, their motion is, 
on the whole, retrograde. 

With regard to the variations in the inclination, it is 
clear, that, when the orbit is symmetrical on each side 
of the disturbing force, all its variations are compensated 
after a revolution of the disturbed body, and are merely 
periodical perturbations in the planet's latitude ; and no 
secular change is induced in the inclination of the orbit. 
When, on the contrary, that orbit is not symmetrical on 
each side of the disturbing force, although many of the 
variations in latitude are transient or periodical, still, 
after a complete revolution of the disturbed body, a 
portion remains uncompensated, which forms a secular 
change in the inclination of the orbit to the plane of the 
ecliptic. It is true, part of this secular change in the 
inclination is compensated by the revolution of the dis- 
turbing body, whose motion has not hitherto been taken 
into the account, so that perturbation compensates per- 



SKCT. III. MEAN MOTION AND MAJOR AXIS. 19 

turbation ; but still, a comparatively permanent change 
is effected in the inclination, which is not compensated 
till the nodes have accomplished a complete revolution. 

The changes in the inclination are extremely minute 
(N. 75), compared with the motion of the nodes, and 
there is the same kind of inseparable connection between 
their secular changes that there is between the variation 
of the eccentricity and the motion of the major axis. 
The nodes and inclinations vary simultaneously, their 
periods are the same, and very great. The nodes of 
Jupiter's orbit, from the action of Saturn alone, require 
36,261 years to accomplish even a tropical revolution. 
In what precedes, the influence of only one disturbing 
body has been considered ; but when the action and re- 
action of the whole system is taken into account, every 
planet is acted upon, and does itself act, in this manner, 
on all the others ; and the joint effect keeps the incli- 
nations and eccentricities in a state of perpetual variation. 
It makes the major axis of all the orbits continually re- 
volve, and causes, on an average, a retrograde motion of 
the nodes of each orbit upon every other. The ecliptic 
(N. 71) itself is in motion from the mutual action of the 
earth and planets, so that the whole is a compound phe- 
nomenon of great complexity, extending through un- 
known ages. At the present time the inclinations of all 
the orbits are decreasing, but so slowly, that the incli- 
nation of Jupiter's orbit is only about six minutes less 
than it was in the age of Ptolemy. 

But, in the midst of all these vicissitudes, the length 
of the major axis and the mean motions of the planets 
remain permanently independent of secular changes. 
They are so connected by Kepler's law, of the squares 
of the periodic times being proportional to the cubes of 
the mean distances of the planets from the sun, that one 
cannot vary without affecting the other. And it is 
proved, that any variations which do take place are 
transient, and depend only on the relative positions of 
the bodies. 

It is true that, according to theory, the radial disturb- 
ing force should permanently alter the dimensions of all 
the orbits, and the periodic times of all the planets, to a 
certain degree. For example, the masses of all the 



20 STABILITY OF THE SYSTEM. SBCT. HI. 

planets revolving within the orbit of any one, such as 
Mars, by adding to the interior mass, increase the at- 
tracting force of the sun, which, therefore, must con- 
tract the dimensions of the orbit of that planet, and di- 
minish its periodic time ; while the planets exterior to 
Mars' orbit must have the contrary effect. But the 
mass of the whole of the planets and satellites taken to- 
gether is so small, when compared with that of the sun, 
that these effects are quite insensible, and could only 
have been discovered by theory. And, as it is certain 
that the length of the major axes and the mean motions 
are not permanently changed by any other power what- 
ever, it may be concluded that they are invariable. 

With the exception of these two elements, it appears 
that all the bodies are in motion, and every orbit in a 
state of perpetual change. Minute as these changes 
are, they might be supposed to accumulate in the course 
of ages, sufficiently to derange the whole order of na- 
ture, to alter the relative positions of the planets, to put 
an end to the vicissitudes of the seasons, and to bring 
about collisions which would involve our whole system, 
now so harmonious, in chaotic confusion. It is natural 
to inquire, what proof exists that nature will be pre- 
served from such a catastrophe ? Nothing can be known 
from observation, since the existence of the human race 
has occupied comparatively but a point in duration, 
while these vicissitudes embrace myriads of ages. The 
proof is simple and conclusive. All the variations of 
the solar system, secular as well as periodic, are ex- 
pressed analytically by the sines and cosines of circular 
arcs (N. 76), which increase with the time ; and, as a 
sine or cosine can never exceed the radius, but must 
oscillate between zero and unity, however much the 
time may increase, it follows that, when the variations 
have accumulated to a maximum, by slow changes, in 
however long a time, they decrease, by the same slow 
degrees, till they arrive at their smallest value, again to 
begin a new course ; thus forever oscillating about a 
mean value. This circumstance, however, would be 
insufficient, were it not for the small eccentricities of 
the planetary orbits, their minute inclinations to the 
plane of the ecliptic, and the revolutions of all the bodies, 



SKCT. HI. STABILITY OF THE SYSTEM. 21 

as well planets as satellites, in the same direction. 
These secure the perpetual stability of the solar system 
(N. 77). The equilibrium, however, would be de- 
ranged, if the planets moved in a resisting medium 
(N. 78) sufficiently dense to diminish their tangential 
velocity, for then both the eccentricities and the major 
axes of the orbits would vary with the time, so that the 
stability of the system would be ultimately destroyed. 
The existence of an ethereal fluid is now proved ; and 
although it is so extremely rare that hitherto its effects 
on the motions of the planets have been altogether in- 
sensible, there can be no doubt that, in the immensity 
of time, it will modify the forms of the planetary orbits, 
and may at last even cause the destruction of our sys- 
tem, which in itself contains no principle of decay, unless 
a rotatory motion from west to east has been given to this 
fluid by the bodies of the solar system, which have all 
been revolving about the sun in that direction for un- 
known ages. This rotation, which seems to be highly 
probable, may even have been coeval with its creation. 
Such a vortex would have no effect on bodies moving 
with it, but it would influence the motions of those re- 
volving in a contraiy direction. It is possible that the 
disturbances experienced by comets which have already 
revealed the existence of this fluid, may also, in time, 
disclose its rotatory motion. 

The form and position of the planetary orbits, and the 
motion of the bodies in the same direction, together with 
the periodicity of the terms in which the inequalities 
are expressed, assure us that the variations of the sys- 
tem are confined within very narrow limits, and that, 
although we do not know the extent of the limits, nor 
the period of that grand cycle which probably embraces 
millions of years, yet they never will exceed what is 
requisite for the stability and harmony of the whole, for 
the preservation of which every circumstance is so beau- 
tifully and wonderfully adapted. 

The plane of the ecliptic itself, though assumed to be 
fixed at a given epoch for the convenience of astronomi- 
cal computation, is subject to a minute secular variation 
of 45"-7, occasioned by the reciprocal action of the plan- 
ets. But, as this is also periodical, and cannot exceed 



22 INVARIABLE PLANE. SECT. III. 

2 42', the terrestrial equator, which is inclined to it at 
an angle of 23 27' 34"- 69, will never coincide with the 
plane of the ecliptic : so there never can be perpetual 
spring (N. 79). The rotation of the earth is uniform ; 
therefore day and night, summer and winter, will con- 
tinue their vicissitudes while the system endures, or is 
undisturbed by foreign causes. 

" Yonder starry sphere 
Of planets and of fix'd, in all her wheels 
Resembles nearest mazes intricate, 
Eccentric, intervolved, yet regular, 
Then most, when most irregular they seem." 

The stability of our system was established by La 
Grange: "a discovery," says Professor Playfair, "that 
must render the name forever memorable in science, 
and revered by those who delight in the contemplation 
of whatever is excellent and sublime." After Newton's 
discovery of the mechanical laws of the elliptical orbits 
of the planets, La Grange's discovery of their periodical 
inequalities is, without doubt, the noblest truth in physi- 
cal astronomy ; and in respect of the doctrine of final 
causes, it may be regarded as the greatest of all. 

Notwithstanding the permanency of our system, the 
secular variations in the planetary orbits would have 
been extremely embarrassing to astronomers when it 
became necessary to compare observations separated by 
long periods. The difficulty was in part obviated, and 
the principle for accomplishing it established, by La 
Place, and has since been extended by M. Poinsot. It 
appears that there exists an invariable plane (N. 80), 
passing through the center of gravity of the system, 
about which the whole oscillates within very narrow 
limits, and that this plane will always remain parallel to 
itself, whatever changes time may induce in the orbits 
of the planets, in the plane of the elliptic, or even in 
the law of gravitation; provided only that our system 
remains unconnected with any other. The position of 
the plane is determined by this property that, if each 
particle in the system be multiplied by the area de- 
scribed upon this plan in a given time, by the projection 
of its radius vector about the common center of gravity 
of the whole, the sum of all these products will be a 



SECT. III. INVARIABLE PLANE. 23 

maximum (N. 81). La Place found that the plane in 
question is inclined to the ecliptic at an angle of nearly 
1 34' 15", and that, in passing through the sun, and 
about midway between the orbits of Jupiter and Saturn, 
it may be regarded as the equator of the solar system, 
dividing it into two parts, wh.ch balance one another in 
all their motions. This plane of greatest inertia, by no 
means peculiar to the solar system, but existing in every 
system of bodies submitted to their mutual attractions 
only, always maintains a fixed position, whence the 
oscillations of the system may be estimated through 
unlimited time. Future astronomers will know, from 
its immutability or variation,, whether the sun and his 
attendants are connected or not w.th the other systems 
of the universe. Should there be no link between them, 
it in.-iy be interred, from the rotation of the sun, that 
the center of gravity (N. 82) of the system situate within 
his mass describes a straight line in this invariable plane 
or great equator of the solar system, which, unaffected 
by the changes of time, will maintain its stability through 
endless ages. But, if the fixed stars, comets, or any 
unknown and unseen bodies, affect our sun and planets, 
the nodes of th s plane w.ll slowly recede on the plane 
of that immense orbit which the sun may describe about 
some most distant center, in a period which it transcends 
the powers of man to determine. There is every rea- 
son to believe that this is the case ; for it is more than 
probable that, remote as the fixed stars are, they in 
some degree influence our system, and that even the 
invariabiLty of this plane is relative, only appearing fixed 
to creatures incapable of estimating its minute and slow 
changes during the small extent of time and space grant- 
ed to the human race. " The development of such 
changes," as M. Poinsot justly observes, " is similar to 
an enormous curve, of which we see so small an arc, 
that we imagine it to be a straight line." If we raise 
our views to the whole extent of the universe, and con- 
sider the stars, together w.th the sun, to be wandering 
bodies, revolving about the common center of creation, 
we may then recognize in the equatorial plane passing 
through the center of gravity of the universe the only 
instance of absolute and eternal repose. 



24 INEQUALITY OF JUPITER AND SATURN. SECT. III. 

All the periodic and secular inequalities deduced from 
the law of gravitation are so perfectly confirmed by 
observation, that analysis has become one of the most 
certain means of discovering the planetary irregularities, 
either when they are too small, or too long in their 
periods, to be detected by other methods. Jupiter and 
Saturn, however, exhibit inequalities which for a long 
time seemed discordant with that law. All observations, 
from those of the Chinese and Arabs down to the pres- 
ent day, prove that for ages the mean motions of Jupiter 
and Saturn have been affected by a great inequality of 
a very long period, forming an apparent anomaly in the 
theory of the planets. It was long known by observa- 
tion that five times the mean motion of Saturn is nearly 
equal to twice that of Jupiter : a relation which the 
sagacity of La Place perceived to be the cause of a 
periodic irregularity in the mean motion of each of these 
planets, which completes its period in nearly 918 years, 
the one being retarded while the other is accelerated ; 
but both the magnitude and period of these quantities 
vary in consequence of the secular variations in the 
elements of the orbits. Suppose the two planets to be 
on the same side of the sun, and all three in the same 
straight line, they are then said to be in conjunction 
(N. 83). Now, if they begin to move at the same time, 
one making exactly five revolutions in its orbit, while the 
other only accomplishes two, it is clear that Saturn, the 
slow-moving body, will only have got through a part of 
its orbit during the time that Jupiter has made one 
whole revolution and part of another, before they be 
again in conjunction. It is found that during this time 
their mutual action is such as to produce a great many 
perturbations which compensate each other, but that 
there still remains a portion outstanding, owing to the 
length of time during which the forces act in the same 
manner ; and if the conjunction always happened in the 
same point of the orbit, this uncompensated inequality 
in the mean motion would go on increasing till the peri- 
odic times and forms of the orbits were completely and 
permanently changed : a case that would actually take 
place if Jupiter accomplished exactly five revolutions in 
the time Saturn performed two. These revolutions 



SICT. Ill ACTION OP PLANETS ON SATELLITES. 25 

are, however, not exactly commensurable ; the points in 
which the conjunctions take place are in advance each 
time as much as 8*37 ; so that the conjunctions do not 
happen exactly in the same points of the orbits till after 
a period of 850 years; and, in consequence of this small 
advance, the planets are brought into such relative posi- 
tions that the inequality which seemed to threaten the 
stability of the system is completely compensated, and 
the bodies, having returned to the same relative positions 
with regard to one another and the sun, begin a new 
course. The secular variations in the elements of the 
orbit increase the period of the inequality to 918 years 
(N. 84). As any perturbation which affects the mean 
motion affects also the major axis, the disturbing forces 
tend to diminish the major axis of Jupiter's orbit and 
increase that of Saturn's during one half of the period, 
and the contrary during the other half. This inequality 
is strictly periodical, since it depends upon the configura- 
tion (N. 85) of the two planets ; and theory is confirmed 
by observation, which shows that, in the course of twenty 
centuries, Jupiter's mean motion has been accelerated 
by about 3 23', and Saturn's retarded by 5 13'. Sev- 
eral instances of perturbations of this kind occur in the 
solar system. One, in the mean motions of the Earth 
and Venus, only amounting to a few seconds, has been 
recently worked out with immense labor by Professor 
Airy. It accomplishes its changes in 240 years, and 
arises from the circumstance of thirteen times the peri- 
odic time of Venus being nearly equal to eight times 
that of the Earth. Small as it is, it is sensible in the 
motions of the Earth. 

It might be imagined that the reciprocal action of such 
planets as have satellites would be different from the 
influence of those that have none. But the distances of 
the satellites from their primaries are incomparably less 
than the distances of the planets from the sun, and from 
one another; so that the system of a planet and its 
satellites moves nearly as if all these bodies were united 
in their common center of gravity. The action of the 
sun, however, in some degree disturbs the motion of the 
satellites about their primary. 

C 



26 THEORY OF JUPITER'S SATELLITES. SECT. IV. 



SECTION IV. 

Theory of Jupiter's Satellites Effects of the Figure of Jupiter upon his 
Satellites Position of theif Orbits Singular Laws among- the Motions 
of the first three Satellites Eclipses of the Satellites Velocity of Light 
Aberration Ethereal Medium Satellites of Saturn and Uranus. 

THE changes which take place in the planetary sys- 
tem are exhibited on a smaller scale by Jupiter and his 
satellites ; and, as the period requisite for the develop- 
ment of the inequalities of these moons only extends to 
a few centuries, it may be regarded as an epitome of 
that grand cycle which will not be accomplished by the 
planets in myriads of ages. The revolutions of the 
satellites about Jupiter are precisely similar to those of 
the planets about the sun : it is true they are disturbed 
by the sun, but his distance is so great, that their 
motions are nearly the same as if they were not under 
his influence. The satellites, like the planets, were 
probably projected in elliptical orbits : but, as the masses 
of the satellites are nearly 100,000 times less than that 
of Jupiter ; and as the compression of Jupiter's sphe- 
roid is so great, in consequence of his rapid rotation, 
that his equatorial diameter exceeds his polar diameter 
by no less than 6000 miles ; the immense quantity of 
prominent matter at his equator must soon have given 
the circular form observed in the orbits of the first and 
second satellites, which its superior attraction will al- 
ways maintain. The third and fourth satellites, being 
farther removed from its influence, revolve in orbits 
with a very small eccentricity. And although the first 
two sensibly move in circles, their orbits acquire a 
small ellipticity, from the disturbances they experience 
(N. 86). 

It has been stated, that the attraction of a sphere on 
an exterior body is the same as if its mass were united 
in one particle in its center of gravity, and therefore 
inversely as the square of the distance. In a spheroid, 
however, there is an additional force arising from the 
bulging mass at its equator, which, not following the 
exact law of gravity, acts as a disturbing force. One 



SECT. IV. EFFECTS OF JUPITER'S COMPRESSION. 27 

effect of this disturbing force in the spheroid of Jupiter 
is, to occasion a direct "motion in the greater axes of the 
orbits of all his satellites, which is more rapid the 
nearer the satellite is to the planet, and very much 
greater than that part of their motion which arises from 
the disturbing action of the sun. The same cause 
occasions the orbits of the satellites to remain nearly in 
tho plane of Jupiter's equator (N. 87), on account of 
which the satellites are always seen nearly in the same 
line (N. 88) ; and the powerful action of that quantity 
of prominent matter is the reason why the motions of 
the nodes of these small bodies are so much more rapid 
than those of the planet. The nodes of the fourth 
satellite accomplish a tropical revolution in 531 years ; 
while those of Jupiter's orbit require no less than 
36,261 years ; a proof of the reciprocal attraction be- 
tween each particle of Jupiter's equator and of the 
satellites. In fact, if the satellites moved exactly in the 
plane of Jupiter's equator, they would not be pulled 
out of that plane, because his attraction would be equal 
on both sides of it. But, as their orbits have a small 
inclination to the plane of the planet's equator, there 
is a want of symmetry, and the action of the protuberant 
matter tends to make the nodes regress by pulling the 
satellites above or below the planes of their orbits ; an 
action which is so great on the interior satellites, that 
the motions of their nodes are nearly the same as if no 
other disturbing force existed. 

The orbits of the satellites do not retain a permanent 
inclination, either to the plane of Jupiter's equator, or 
to that of his orbit, but to certain planes passing between 
the two, and through their intersection. These have a 
greater inclination to his equator the farther the satel- 
lite is removed, owing to the influence of Jupiter's 
compression ; and they have a slow motion correspond- 
ing to secular variations in the planes of Jupiter's orbit 
and equator. 

The satellites are not only subject to periodic and 
secular inequalities from their mutual attraction, similar 
to those which affect the motions and orbits of the 
planets, but also to others peculiar to themselves. Of 
the periodic inequalities arising from their mutual at- 



28 PERTURBATIONS OF THE SATELLITES. SECT. IV. 

traction, the most remarkable take place in the angular 
motions (N. 89) of the three nearest to Jupiter, the 
second of which receives from the first a perturbation 
similar to that which it produces in the third ; and it 
experiences from the third a perturbation similar to that 
which it communicates to the first. In the eclipses 
these two inequalities are combined into one, whose 
period is 437-659 da >' s . The variations peculiar to the 
satellites arise from the secular inequalities occasioned 
by the action of the planets in the form and position of 
Jupiter's orbit, and from the displacement of his equator. 
It is obvious that whatever alters the relative positions 
of the sun, Jupiter, and his satellites, must occasion a 
change in the directions and intensities of the forces, 
which will affect the motions and orbits of the satellites. 
For this reason the secular variations in the eccen- 
tricity of Jupiter's orbit occasion secular inequalities in 
the mean motions of the satellites, and in the motions 
of the nodes and apsides of their orbits. The displace- 
ment of the orbit of Jupiter, and the variation in the 
position of his equator, also aflfect these small bodies 
(N. 90). The plane of Jupiter's equator is inclined to 
the plane of his orbit at an angle of 3 5' 30", so that 
the action of the sun and of the satellites themselves 
produces a nutation and precession (N. 91) in his equa- 
tor, precisely similar to that which takes place in the 
rotation of the earth, from the action of the sun and 
moon. Hence the protuberant matter at Jupiter's equa- 
tor is continually changing its position with regard to 
the satellites, and produces corresponding mutations in 
their motions. And, as the cause must be proportional 
to the effect, these inequalities afford the means, not 
only of ascertaining the compression of Jupiter's sphe- 
roid, but they prove that his mass is not homogeneous. 
Although the apparent diameters of the satellites are 
too small to be measured, yet their perturbations give 
the values of their masses with considerable accuracy 
a striking proof of the power of analysis. 

A singular law obtains among the mean motions and 
mean longitudes of the first three satellites. It appears 
from observation that the mean motion of the first 
satellite, plus twice that of the third, is equal to three 



SKCT, IV. ECLIPSES OP THE SATELLITES. 29 

times that of the second ; and that the mean longitude 
of the first satellite, minus three times that of the 
second, plus twice that of the third, is always equal to 
two right angles. It is proved by theory, that if these 
relations had only been approximate when the satellites 
were first launched into space, their mutual attractions 
would have established and maintained them, notwith- 
standing the secular inequalities to which they are 
liable. They extend to the synodic motions (N. 92) of 
the satellites ; consequently they affect then* eclipses, 
and have a very great influence on their whole theory. 
The satellites move so nearly in the plane of Jupiter's 
equator, which has a very small inclination to his orbit, 
that the first three are eclipsed at each revolution by 
the shadow of the planet, which is much larger than 
the shadow of the moon : the fourth satellite is not 
eclipsed so frequently as the others. The eclipses 
take place close to the disc of Jupiter when he is near 
opposition (N. 93); but at times his shadow is so pro- 
jected with regard to the earth, that the third and 
fourth satellites vanish and reappear on the same side 
of the disc (N. 94). These eclipses are in all respects 
similar to those of the moon : but, occasionally, the 
satellites eclipse Jupiter, sometimes passing like obscure 
spots across his surface, resembling annular eclipses of 
the sun, and sometimes like a bright spot traversing one 
of his dark belts. Before opposition, the shadow of the 
satelb'te, like a round black spot, precedes its passage 
over the disc of the planet ; and after opposition, the 
shadow follows the satellite. 

In consequence of the relations already mentioned in 
the mean motions and mean longitudes of the first three 
satellites, they never can be all eclipsed at the same 
time. For when the second and third are in one direc- 
tion, the first is in the opposite direction ; consequently, 
when the first is eclipsed, the other two must be be- 
tween the sun and Jupiter. The instant of the begin- 
ning or end of an eclipse of a satellite marks the same 
instant of absolute time to all the inhabitants of the 
earth; therefore, the time of these eclipses observed 
by a traveler, when compared with the time of the 
eclipse computed for Greenwich, or any other fixed 
c2 



30 ABERRATION. SECT. IV. 

meridian (N. 95), gives the difference of the meridians 
in time, and, consequently, the longitude of the place of 
observation. The eclipses of Jupiter's satellites have 
been the means of a discovery which, though not so 
immediately applicable to the wants of man, unfolds 
one of the properties of light that medium without 
whose cheering influence all the beauties of the creation 
would have been to us a blank. It is observed, that 
those eclipses of the first satellite, which happen when 
Jupiter is near conjunction (N. 96), are later by 16 m 
26"6 than those which take place when the planet is in 
opposition. As Jupiter is nearer to us when in opposi- 
tion by the whole breadth of the earth's orbit than 
when in conjunction, this circumstance is attributed to 
the time employed by the rays of light in crossing the 
earth's orbit, a distance of about 191X000,000 of miles ; 
whence it is estimated that light travels at the rate of 
190,000 miles in one second. Such is its velocity, that 
the earth, moving at the rate of nineteen miles in a 
second, would take two months to pass through a dis- 
tance which a ray of light would dart over in eight 
minutes. The subsequent discovery of the aberration 
of light confirmed this astonishing result. 

Objects appear to be situated in the direction of the 
rays which proceed from them. Were light propagated 
instantaneously, every object, whether at rest or in mo- 
tion, would appear in the direction of these rays ; but 
as light takes some time to travel, we see Jupiter in 
conjunction, by means of rays that left him 16 m 26 8> 6 be- 
fore ; but, during that time, we have changed our posi- 
tion, in consequence of the motion of the earth in its 
orbit : we therefore refer Jupiter to a place in which he 
is not. His true position is in the diagonal (N. 97) of 
the parallelogram, whose sides are in the ratio of the 
velocity of light to the velocity of the earth in its orbit, 
which is as 190,000 to 19, or 10,000 to 1. In conse- 
quence of the aberration of light, the heavenly bodies 
seem to be in places in which they are not. In fact, if 
the earth were at rest, rays from a star would pass along 
the axis of a telescope directed to it; but if the earth 
were to begin to move in its orbit, with its usual velocity, 
these rays would strike against the side of the tube ; it 



SKCT. IV. VELOCITY OF LIGHT. 31 

would, therefore, be necessary to incline the telescope 
a little, in order to see the star. The angle contained 
between the axis of the telescope and a line drawn to 
the true place of the star, is its aberration, which varies 
in quantity and direction in different parts of the earth's 
orbit ; but as it is only 20"-36, it is insensible in ordinary 
cases (N. 98). 

The velocity of light deduced from the observed aber- 
ration of the fixed stars perfectly corresponds with that 
given by the eclipses of the first satellite. The same 
result, obtained from sources so different, leaves not a 
doubt of its truth. Many such beautiful coincidences, 
derived from circumstances apparently the most un- 
promising and dissimilar, occur in physical astronomy, 
and prove connections which we might otherwise be un- 
able to trace. The identity of the velocity of light, at 
the distance of Jupiter, and on the earth's surface, shows 
that its velocity is uniform ; and if light consists in the 
vibrations of an elastic fluid or ether filling space, a hy- 
pothesis which accords best with observed phenomena, 
the uniformity of its velocity shows that the density 
of the fluid throughout the whole extent of the solar 
system must be proportional to its elasticity (N. 99). 
Among the fortunate conjectures which have been con- 
firmed by subsequent experience, that of Bacon is not 
the least remarkable. " It produces in me," says the 
restorer of true philosophy, " a doubt whether the face 
of the serene and starry heavens be seen at the instant 
it really exists, or not till some time later : and whether 
there be not, with respect to the heavenly bodies, a true 
time and an apparent time, no less than a true place 
and an apparent place, as astronomers say, on account 
of parallax. For it seems incredible that the species or 
rays of the celestial bodies can pass through the im- 
mense interval between them and us in an instant, or 
that they do not even require some considerable portion 
of time." 

Great discoveries generally lead to a variety of con- 
clusions : the aberration of light affords a direct proof of 
the motion of the earth in its orbit ; and its rotation is 
proved by the theory of falling bodies, since the centri- 
fugal force it induces retards the oscillations of the pen- 



32 SATELLITES OF JUPITER AND URANUS. SKCT. IV. 

dulum (N. 100) in going from the pole to the equator. 
Thus a high degree of scientific knowledge has been 
requisite to dispel the errors of the senses. 

The little that is known of the theories of the satel- 
lites of Saturn and Uranus, is, in all respects, similar to 
that of Jupiter. Saturn is accompanied by seven satel- 
lites, the most distant of which is about the size of the 
planet Mars. Its orbit has a sensible inclination to the 
plane of the ring ; but the great compression of Saturn 
occasions the other satellites to move nearly in the plane 
of his equator. So many circumstances must concur to 
render the two interior satellites visible, that they have 
very rarely been seen. They move exactly at the edge 
of the ring, and their orbits never deviate from its plane. 
In 1789, Sir William Herschel saw them, like beads, 
threading the slender line of light which the ring is re- 
duced to, when seen edgewise from the earth. And 
for a short time he perceived them advancing off it at 
each end, when turning round in their orbits. The 
eclipses of the exterior satellites only take place when 
the ring is in this position. Of the situation of the equa- 
tor of Uranus we know nothing, nor of his compression ; 
but the orbits of his satellites are nearly perpendicular 
to the plane of the ecliptic ; and, by analogy, they ought 
to be in the plane of his equator. Uranus is so remote 
that he has more the appearance of a planetary nebula 
than a planet, which renders it extremely difficult to 
distinguish the satellites at all ; and quite hopeless with- 
out such a telescope as is rarely to be met with even in 
observatories. Sir William Herschel discovered six, 
and determined the motions of two of them ; but from 
that time the position of the planet has been such as to 
render farther observations impossible. The subject 
has recently occupied the attention of his son, who has 
found evidence of the general correctness of his father's 
views, and has been enabled to determine the elements 
of the motions of these minute objects with more accu- 
racy. The first satellite performs its revolution about 
Uranus in 8 d 16 h 56 ra 28 s -6 ; and the second satellite ac- 
complishes its period in 13 d ll h 7 m 12 B 6. The orbits of 
both seem to have an inclination of about 101 -2 to the 
plane of the ecliptic ; and their motions offer the singu- 



SECT. V LUNAR THEORY 33 

Jar phenomenon of being retrograde, or from east to 
west ; while all the planets and the other satellites re- 
volve in the contrary direction. Sir John Herschel could 
not perceive the smallest indication of a ring. 



SECTION V. 

Lunar Theory Periodic Perturbations of the Moon Equation of Center- 
Evection Variation Annual Equation Direct and Indirect Action of 
Planets The Moon's Action on the Earth disturbs her own Motion- 
Eccentricity and Inclination of Lunar Orbit Invariable Acceleration 
Secular Variation in Nodes and Perigee Motion of Nodes and Perigee 
inseparably connected with the Acceleration Nutation of Lunar Orbit 
Form and Internal Structure of the Earth determined from it Lunar, 
Solar, and Planetary Eclipses Occultations and Lunar Distances Mean 
Distance of the Sun from the Earth obtained from Lunar Theory Abso- 
lute Distances of the Planets, how Found. 

OUR constant companion, the moon, next claims our 
attention. Several circumstances concur to render her 
motions the most interesting, and at the same time the 
most difficult to investigate, of all the bodies of our sys- 
tem. In the solar system, planet troubles planet ; but in 
the lunar theory, the sun is the great disturbing cause ; 
his vast distance being compensated by his enormous 
magnitude, so that the motions of the moon are more 
irregular than those of the planets ; and, on account of 
the great ellipticity of her orbit, and the size of the sun, 
the approximations to her motions are tedious and diffi- 
cult, beyond what those unaccustomed to such investiga- 
tions could imagine. The average distance of the moon 
from the center of the earth is only 237,360 miles, so 
that her motion among the stars is perceptible in a few 
hours. She completes a circuit of the heavens in 
27 d 7 h 43 m 4 8 -7, moving in an orbit whose eccentricity is 
about 12,985 miles. The moon is about four hundred 
times nearer to the earth than the sun. The proximity 
of the moon to the earth keeps them together. For so 
great is the attraction of the sun, that if the moon were 
farther from the earth, she would leave it altogether, and 
would revolve as an independent planet about the sun. 

The disturbing action (N. 101) of the sun on the moon 
is equivalent to three forces. The first, acting in the 
direction of the line joining the moon and earth, in- 
3 



34 DISTURBING ACTION OF THE SUN. SECT. V. 

ereases or diminishes her gravity to the earth. The 
second, acting in the direction of a tangent to her orbit, 
disturbs her motion in longitude ; and the .third, acting 
perpendicularly to the plane of her orbit, disturbs her 
motion in latitude that is, it brings her nearer or re- 
moves her farther from the plane of the ecliptic than 
she would otherwise be. The periodic perturbations' 
in the moon arising from these forces, are perfectly sim- 
ilar to the periodic perturbations of the planets. But 
they are much greater and more numerous ; because 
the sun is so large, that many inequalities which are 
quite insensible in the motions of the planets, are of 
great magnitude in those of the moon. Among the in- 
numerable periodic inequalities to which the moon's 
motion in longitude is liable, the most remarkable are, 
the Equation of the Center, which is the difference be- 
tween the moon's mean and true longitude, the Evec- 
tion, the Variation, and the Annual Equation. The 
disturbing force which acts in the line joining the moon 
and earth produces the Evection : it diminishes the ec- 
centricity of the lunar orbit in conjunction and opposi- 
tion, thereby making it more circular, and augments it 
in quadrature, which consequently renders it more ellip- 
tical. The period of this inequality is less than thirty- 
two days. Were the increase and diminution always 
the same, the Evection would only depend upon the 
distance of the moon from the sun ; but its absolute 
value also varies with her distance from the perigee 
(N. 102) of her orbit. Ancient astronomers, who ob- 
served the moon solely with a view to the prediction of 
eclipses, which can only happen in conjunction and oppo- 
sition, where the eccentricity is diminished by the Evec- 
tion, assigned too small a value to the ellipticity of her 
orbit (N. 193). The Evection was discovered by Ptole- 
my from observation, about A.D. 140. The variation 
produced by the tangential disturbing force, which is 
at its maximum when the moon is 45 distant from the 
sun, vanishes when that distance amounts to a quadrant, 
and also when the moon is in conjunction and opposi- 
tion ; consequently, that inequality never could have 
been discovered from the eclipses : its period is half a 
lunar month (N. 104). The Annual Equation depends 



SBCT. V. DISTURBING ACTION OF THE PLANETS. 35 

upon the sun's distance from the earth : it arises from 
the moon's motion being accelerated when that of the 
earth is retarded, and vice versa for when the earth is 
in its perihelion, the lunar orbit is enlarged by the ac- 
tion of the sun ; therefore, the moon requires more 
time to perform her revolution. But, as the earth ap- 
proaches its aphelion, the moon's orbit contracts, and 
less time is necessaiy to accomplish her motion its 
period, consequently, depends upon the time of the 
year. In the eclipses, the annual equation combines 
with the equation of the center of the terrestrial orbit, 
so that ancient astronomers imagined the earth's orbit 
to have a greater eccentricity than modern astronomers 
assign to it. 

The planets disturb the motion of the moon both 
directly and indirectly : their action on the earth alters 
its relative position with regard to the sun and moon, 
and occasions inequalities in the moon's motion, which 
are more considerable than those arising from their 
direct action ; for the same reason the moon, by disturb- 
ing the earth, indirectly disturbs her own motion. Nei- 
ther the eccentricity of the lunar orbit, nor its mean 
inclination to the plane of the ecliptic, have experienced 
any changes from secular inequalities; for, although 
the mean action of the sun on the moon depends upon 
the inclination of the lunar orbit to the ecliptic, and the 
position of the ecliptic is subject to a secular inequality, 
yet analysis shows that it does not occasion a secular 
variation in the inclination of the lunar orbit, because 
the action of the sun constantly brings the moon's orbit 
to the same inclination to the ecliptic. The mean mo- 
tion, the nodes, and the perigee, however, are subject 
to very remarkable variations. 

From the eclipse observed by the Chaldeans at Baby- 
lon, on the 19th of March, seven hundred and twenty- 
one years before the Christian era, the place of the 
moon is known from that of the sun at the instant of 
opposition (N. 83), whence her mean longitude may be 
found. But the comparison of this mean longitude with 
another mean longitude, computed back for the instant 
of the eclipse from modern observations, shows that the 
moon performs her revolution round the earth more 



36 ACCELERATION. SECT. V. 

rapidly and in a shorter time now than she did formerly, 
and that the acceleration in her mean motion has been 
increasing from age to age as the square of the time 
(N. 105). All ancient and intermediate eclipses confirm 
this result. As the mean motions of the planets have 
no secular inequalities, this seemed to be an unaccount- 
able anomaly. It was at one time attributed to the re- 
sistance of an ethereal medium pervading space, and at 
another to the successive transmission of the gravitating 
force. But as La Place proved that neither of these 
causes, even if they exist, have any influence on the 
motions of the lunar perigee (N. 102) or nodes, they 
could not affect the mean motion ; a variation in the 
mean motion from such causes being inseparably con- 
nected with the variations in the motions of the perigee 
and nodes. That great mathematician, in studying the 
theory of Jupiter's satellites, perceived that the secular 
variation in the elements of Jupiter's orbit, from the 
action of the planets, occasions corresponding changes 
in the motions of the satellites, which led him to sus- 
pect that the acceleration in the mean motion of the 
moon might be connected with the secular variation in 
the eccentricity of the terrestrial orbit. Analysis has 
shown that he assigned the true cause of the acceleration. 
It is proved that the greater the eccentricity of the 
terrestrial orbit, the greater is the disturbing action of 
the sun on the moon. Now as the eccentricity has 
been decreasing for ages, the effect of the sun in dis- 
turbing the moon has been diminishing during that time. 
Consequently the attraction of the earth has had a more 
and more powerful effect on the moon, and has been 
continually diminishing the size of the lunar orbit. So 
that the moon's velocity has been gradually augmenting 
for many centuries to balance the increase of the earth's 
attraction. This secular increase in the moon's velocity 
is called the Acceleration, a name peculiarly appropriate 
at present, and which will continue to be so for a vast 
number of ages ; because, as long as the earth's eccen- 
tricity diminishes, the moon's mean motion will be ac- 
celerated ; but when the eccentricity has passed its 
minimum, and begins to increase, the mean motion will 
be retarded from age to age. The secular acceleration 



SECT. V. MOTION OF NODES AND PERIGEE. 37 

is now about ll"-9, but its effect on the moon's place 
increases as the square of the time. It is remarkable 
that the action of the planets, thus reflected by the sun 
to the moon, is much more sensible than their direct 
action either on the earth or moon. The secular dimi- 
nution in the eccentricity, which has not altered the 
equation of the center of the sun by eight minutes since 
the earliest recorded eclipses, has produced a variation 
of about 1 48' in the moon's longitude, and of 7 12' in 
her mean anomaly (N. 106). 

The action of the sun occasions a rapid but variable 
motion in the nodes and perigee of the lunar orbit. 
Though the nodes recede during the greater part of the 
moon's revolution, and advance during the smaller, they 
perform then* sidereal revolution in 6793 d 9 h 23 ra 9"-3 ; 
and the perigee accomplishes a revolution in 3232 J 13 h 
48 m 29 s - 6, or a little more thart nine years, notwith- 
standing its motion is sometimes retrograde and some- 
times direct : but such is the difference between the 
disturbing energy of the sun and that of all the planets 
put together, that it requires no less than 109,830 years 
for the greater axis of the terrestrial orbit to do the 
same, moving at the rate of IT'-S annually. The form 
of the earth has no sensible effect either on the lunar 
nodes or apsides. It is evident that the same secular 
variation which changes the sun's distance from the 
earth, and occasions the acceleration in the moon's mean 
motion, must affect the nodes and perigee. It conse- 
quently appears, from theory as well as observation, that 
both these elements are subject to a secular inequality, 
arising from the variation in the eccentricity of the 
earth's orbit, which connects them with the Acceleration, 
so that both are retarded when the mean motion is an- 
ticipated. The secular variations in these three ele- 
ments are in the ratio of the numbers 3, 0-735, and 1 ; 
whence the three motions of the moon, with regard to 
the sun, to her perigee, and to her nodes, are continu- 
ally accelerated, and their secular equations are as the 
numbers 1, 4-702, and 0-612. A comparison of ancient 
eclipses observed by the Arabs, Greeks, and Chaldeans, 
imperfect as they are, with modern observations, con- 
firms these results of analysis. Future ages will de- 
D 



38 NUTATION OF LUNAR ORBIT. SECT. V. 

velop these great inequalities, which at some most 
distant period will amount to many circumferences 
(N. 107). They are, indeed, periodic; but who shall 
tell their period ? Millions of years must elapse before 
that great cycle is accomplished. 

. The moon is so near, that the excess of matter at the 
earth's equator occasions periodic variations in her lon- 
gitude, and also that remarkable inequality in her lati- 
tude, already mentioned as a nutation in the lunar orbit, 
which diminishes its inclination to the ecliptic when the 
moon's ascending node coincides with the equinox of 
spring, and augments it when that node coincides with 
the equinox of autumn. As the cause must be propor- 
tional to the effect, a comparison of these inequalities, 
computed from theory, with the same given by obser- 
vation, shows that the compression of the terrestrial 
spheroid, or the ratio of the difference between the 
polar and the equatorial diameters, to the diameter of 
the equator, is ^37.7^ It is proved analytically, that if 
a fluid mass of homogeneous matter, whose particles 
attract each other inversely as the squares of the dis- 
tance, were to revolve about an axis as the earth does, 
it would assume the form of a spheroid whose compres- 
sion is -^1^. Since that is not the case, the earth can- 
not be Homogeneous, but must decrease in density from 
its center to its circumference. Thus the moon's 
eclipses show the earth to be round ; and her inequali- 
ties not only determine the form, but even the internal 
structure of our planet ; results of analysis which could 
not have been anticipated. Similar inequalities in the 
motions of Jupiter's satellites prove that his mass is not 
homogeneous, and that his compression is T ^. ? . His 
equatorial diameter exceeds his polar diameter by about 
6000 miles. 

The phases (N. 108) of the moon, which vary from 
a slender silvery crescent soon after conjunction to a 
complete circular disc of light in opposition, decrease by 
the same degrees till the moon is again enveloped in 
the morning beams of the sun. These changes regulate 
the returns of the eclipses. Those .of the sun can only 
happen in conjunction, when the moon, coming between 
the earth and the sun, intercepts his light. Those of 



SECT. V. LUNAR ECLIPSES. 39 

the moon are occasioned by the earth intervening be- 
tween the sun and moon when in opposition. As the 
earth is opaque and nearly spherical, it throws a conical 
shadow on the side of the moon opposite to the sun, the 
axis of which passes through the centers of the sun and 
earth (N. 109). The length of the shadow terminates 
at the point where the apparent diameters (N. 110) 
of the sun and earth would be the same. When the 
moon is in opposition, and at her mean distance, the 
diameter of the sun would be seen from her center 
under an angle of 1918"-1. That of the earth would 
appear under an angle of 6908"-3. So that the length 
of the shadow is at least three times and a half greater 
than the distance of the moon from the earth, and the 
breadth of the shadow, where it is traversed by the 
moon, is about eight-thirds of the lunar diameter. Hence 
the moon would be eclipsed every time she is in oppo- 
sition, were it not for the inclination of her orbit to the 
plane of the ecliptic, in consequence of which the moon 
when in opposition is either above or below the cone of 
the earth's shadow, except when in or near her nodes. 
Her position with regard to them occasions all the vari- 
eties in the lunar eclipses. Every point of the moon's 
surface successively loses the light of different parts of 
the sun's disc before being eclipsed. Her brightness 
therefore gradually diminishes before she plunges into 
the earth's shadow. The breadth of the space occupied 
by the penumbra (N. Ill) is equal to the apparent di- 
ameter of the sun, as seen from the center of the moon. 
The mean duration of a revolution of the sun, with re- 
gard to the node of the lunar orbit, is to the duration of 
a synodic revolution (N. 112) of the moon as 223 to 19. 
So that, after a period of 223 lunar months, the sun and 
moon would return to the same relative position with 
regard to the node of the moon's orbit, and therefore 
the eclipses would recur in the same order, were not 
the periods altered by irregularities in the motions of 
the sun and moon. In lunar eclipses, our atmosphere 
bends the sun's rays which pass through it all round 
into the cone of the earth's shadow. And as the hori- 
zontal refraction (N. 113) or bending of the rays sur- 
passes half the sum of the semidiameters of the sun 



40 LUNAR AND SOLAR ECLIPSES. SECT. V. 

and moon, divided by their mutual distance, the center 
of the lunar disc, supposed to be in the axis of the 
shadow, would receive the rays from the same point of 
the sun, round all sides of the earth, so that it would be 
more illuminated than in full moon, if the greater por- 
tion of the light were not stopped or absorbed by the 
atmosphere. Instances are recorded where this feeble 
light has been entirely absorbed, so that the moon has 
altogether disappeared in her eclipses. 

The sun is eclipsed when the moon intercepts his 
rays (N. 114). The moon, though incomparably smaller 
than the sun, is so much nearer the earth, that her 
apparent diameter differs but little from his, but both 
are liable to such variations, that they alternately sur- 
pass one another. Were the eye of a spectator in the 
same straight line with the centers of the sun and moon, 
he would see the sun eclipsed. If the apparent diame- 
ter of the moon surpassed that of the sun, the eclipse 
would be total. If it were less, the observer would see 
a ring of light round the disc of the moon, and the 
eclipse would be annular, as it was on the 17th of May, 
1836. If the center of the moon should not be in the 
straight line joining the centers of the sun and the eye 
of the observer, the moon might only eclipse a part of 
the sun. The variation, therefore, in the distances of 
the sun and moon from the center of the earth, and of 
the moon from her node at the instant of conjunction, 
occasions great varieties in the solar eclipses. Besides, 
the height of the moon above the horizon changes her 
apparent diameter, and may augment or diminish the 
apparent distances of the centers of the sun and moon, 
so that an eclipse of the sun may occur to the inhabi- 
tants of one country, and not to those of another. In 
this respect the solar eclipses differ from the lunar, 
which are the same for every part of the earth where 
the moon is above the horizon. In solar eclipses, the 
light reflected by the atmosphere diminishes the obscu- 
rity they produce. Even in total eclipses the higher 
part of the atmosphere is enlightened by a part of the 
sun's disc, and reflects its rays to the earth. The whole 
disc of the new moon is frequently visible from atmos- 
pheric reflection. 



S.CT. V ECLIPSES OF PLANETS. 41 

A phenomenon altogether unprecedented occurred 
during the total eclipse of the sun which happened on 
the 8th of July, 1842. The moon was like a black 
patch on the sky surrounded by a faint whitish light 
about the eighth of the moon's diameter in breadth, in 
which three red flames appeared in form like the teeth 
of a saw ; from what cause they originated, or what 
they were, is totally unknown. 

Planets sometimes eclipse one another. On the 17th 
of May, 1737, Mercury was eclipsed by Venus near 
their inferior conjunction ; Mars passed over Jupiter on 
the 9th of January, 1591 ; and on the 30th of October, 
1825, the moon eclipsed Saturn. These phenomena, 
however, happen very seldom, because all the planets, 
or even a part of them, are very rarely seen in con- 
junction at once ; that is, in the same part of the heav- 
ens at the same time. More than 2500 years before 
our era, the five great planets were in conjunction. On 
the 15th of September, 1186, a similar assemblage took 
place between the constellations of Virgo and Libra; 
and in 1801, the moon, Jupiter, Saturn, and Venus 
were united in the heart of the Lion. These conjunc- 
tions are so rare, that Lalande has computed that more 
than seventeen millions of millions of years separate the 
epochs of the contemporaneous conjunctions of the six 
great planets. 

The motions of the moon have now become of more 
importance to the navigator and geographer than those 
of any other heavenly body, from the precision with 
which terrestrial longitude is deter mined "by occultations 
of stars, and by lunar distances. In consequence of the 
retrograde motion of the nodes of the lunar orbit, at the 
rate of 3' 10"-64 daily, these points make a tour of the 
heavens in a little more than eighteen years and a half. 
This causes the moon to move round the earth in a kind 
of spiral, so that her disc at different times passes over 
every point in a zone of the heavens extending rather 
more than 5 9' on each side of the ecliptic. It is there- 
fore evident, that at one time or other she must eclipse 
every star and planet she meets with in this space. 
Therefore the occultation of a star by the moon is a phe- 
nomenon of frequent occurrence. The moon seems to 



42 DISTANCES, HOW FOUND. SECT. V. 

pass over the star, which almost instantaneously vanishes 
at one side of her disc, and after a short time as suddenly 
reappears on the other. A lunar distance is the ob- 
served distance of the moon from the sun, or from a 
particular star or planet, at any instant. The lunar the- 
ory is brought to such perfection, that the times of these 
phenomena, observed under any meridian when com- 
pared with those computed for Greenwich in the Nauti- 
cal Almanac, give the longitude of the observer within a 
few miles (N. 95). 

From the lunar theory, the mean distance of the sun 
from the earth, and thence the whole dimensions of the 
solar system, are known. For the forces which retain 
the earth and moon in their orbits are respectively pro- 
portional to the radii vectores of the earth and moon, 
each being divided by the square of its periodic time. 
And as the lunar theory gives the ratio of the forces, 
the ratio of the distances of the sun and moon from 
the earth is obtained. Hence it appears that the sun's 
mean distance from the earth is 396, or nearly 400 
times greater than that of the moon. The method of 
finding the absolute distances of the celestial bodies in 
miles, is in fact the same with that employed in meas- 
uring the distances of terrestrial objects. From the 
extremities of a known base (N. 115), the angles which 
the visual rays from the object form with it, are meas- 
ured ; their sum subtracted from two right angles gives 
the angle opposite the base ; therefore, by trigonometry, 
all the angles and sides of the triangle may be computed 
consequently the distance of the object is found. The 
angle under which the base of the triangle is seen from 
the object is the parallax of that object. It evidently in- 
creases and decreases with the distance. Therefore the 
base must be very great indeed to be visible from the 
celestial bodies. The globe itself, whose dimensions are 
obtained by actual admeasurement, furnishes a standard 
of measures, with which we compare the distances, 
masses, densities, and volumes of the sun and planets. 



SECT. VI. THEORETICAL FORM OF THE EARTH. 43 



SECTION VI. 

Form of the Earth and Planets Figure of a Homogeneous Spheroid in 
Rotation Figure of a Spheroid of Variable Density Figure of the 
Earth, supposing it to be an Ellipsoid of Revolution Mensuration of a 
Degree of the Meridian Compression and Size of the Earth from 
Degrees of Meridian Figure of Earth from the Pendulum. 

THE theoretical investigation of the figure of the earth 
and planets is so complicated, that neither the geometry 
of Newton, nor the refined analysis of La Place, has 
attained more than an approximation. It is only within 
a few years that a complete and finite solution of that 
difficult problem has been accomplished by our distin- 
guished countryman Mr. Ivory. The investigation has 
been conducted by successive steps, beginning with a 
simple case, and then proceeding to the more difficult. 
But in all, the forces which occasion the revolutions of 
the earth and planets are omitted, because, by acting 
equally upon all the particles, they do not disturb their 
mutual relations. A fluid mass of uniform density, whose 
particles mutually gravitate to each other, will assume 
the form of a sphere when at rest. But if the sphere 
begins to revolve, every particle will describe a circle 
(N. 116), having its center in the axis of revolution. 
The planes of all these circles will be parallel to one 
another and perpendicular to the axis, and the particles 
will have a tendency to fly from that axis in consequence 
of the centrifugal force arising from the velocity of rota- 
tion. The force of gravity is everywhere perpendicular 
to the surface (N. 117), and tends to the interior of the 
fluid mass ; whereas the centrifugal force acts perpen- 
dicularly to the axis of rotation, and is directed to the 
exterior. And as its intensity diminishes with the dis- 
tance from the axis of rotation, it decreases from the 
equator to the poles, where it ceases. Now it is clear 
that these two forces are in direct opposition to each 
other in the equator alone, and that gravity is there di- 
minished by the whole eflect of the centrifugal force, 
whereas, in every other part of the fluid, the centrifugal 
force is resolved into two parts, one of which, being per- 
pendicular to the surface, diminishes the force of grav- 



44 ROTATION OF A FLUID MASS. SECT. VI. 

ity ; but the other, being at a tangent to the surface, 
urges the particles toward the equator, where they ac- 
cumulate till their numbers compensate the diminution 
of gravity, which makes the mass bulge at the equator, 
and become flattened at the poles. It appears, then, that 
the influence of the centrifugal force is most powerful at 
the equator, not only because it is actually greater there 
than elsewhere, but because its whole effect is employed 
in diminishing gravity, whereas, in every other point of 
the fluid mass, it is only a part that is so employed. For 
both these reasons, it gradually decreases toward the 
poles, where it ceases. On the contraiy, gravity is least 
at the equator, because the particles are farther from 
the center of the mass, and increases toward the poles, 
where it is greatest. It is evident, therefore, that, as 
the centrifugal force is much less than the force of grav- 
ity gravitation, which is the difference between the 
two, is least at the equator, and continually increases 
toward the poles, where it is a maximum. On these 
principles Sir Isaac Newton proved that a homogeneous 
fluid (N. 118) mass in rotation assumes the form of an 
ellipsoid of revolution (N. 119), whose compression is 
-5 . Such, however, cannot be the form of the earth, 
because the strata increase in density toward the center. 
The lunar inequalities also prove the earth to be so con- 
structed ; it was requisite, therefore, to consider the fluid 
mass to be of variable density. Including this condition, 
it has been found that the mass, when in rotation, would 
still assume the form of an ellipsoid of revolution ; that 
the particles of equal density would arrange themselves 
in concentric elliptical strata (N. 120), the most dense 
being in the center; but. that the compression or flat- 
tening would be less than in the case of the homogene- 
ous fluid. The compression is still less when the mass 
is considered to be, as it actually is, a solid nucleus, de- 
creasing regularly in density from the center to the sur- 
face, and partially covered by the ocean, because the 
solid parts, by their cohesion, nearly destroy that part 
of the centrifugal force which gives the particles a ten- 
dency to accumulate at the equator, though not alto- 
gether ; otherwise the sea, by the superior mobility of 
its particles, would flow toward the equator and leave 



SCT. VI. FORM OF THE EARTH. 45 

the poles dry. Beside, it is well known, that the con- 
tinents at the equator are more elevated than they are 
in higher latitudes. It is also necessary for the equili- 
brium of the ocean, that its density should be less than 
the mean density of the earth, otherwise the continents 
would be perpetually liable to inundations from storms, 
and other causes. On the whole, it appears from the- 
ory, that a horizontal line passing round the earth 
through both poles, must be nearly an ellipse, having its 
major axis in the plane of the equator, and its minor 
axis coincident with the axis of the earth's rotation 
(N. 121). It is easy to show, in a spheroid whose 
strata are elliptical, that the increase in the length of 
the radii (N. 122), the decrease of gravitation, and the 
increase in the length of the arcs of the meridian, cor- 
responding to angles of one degree, from the poles to 
the equator, are all proportional to the square of the co- 
sine of the latitude (N. 123). These quantities are so 
connected with the ellipticity of the spheroid that the 
total increase in the length of the radii is equal to the 
compression or flattening, and the total diminution in the 
length of the arcs is equal to the compression, multi- 
plied by three times the length of an arc of one degree 
at the equator. Hence, by measuring the meridian 
curvature of the earth, the compression, and conse- 
quently its figure, become known. This, indeed, is as- 
suming the earth to be an ellipsoid of revolution, but 
the actual measurement of the globe will show how far 
it corresponds with that solid in figure and constitution. 

The courses of the great rivers, which are in general 
navigable to a considerable extent, prove that the curva- 
ture of the land differs but little from that of the ocean ; 
and as the heights of the mountains and continents are 
inconsiderable when compared with the magnitude of 
the earth, its figure is understood to be determined by 
a surface at every point perpendicular to the direction 
of gravitation, or of the plumb-line, and is the same 
which the sea would have, if it were continued all round 
the earth beneath the continents. Such is the figure 
that has been measured in the following manner : 

A terrestrial meridian is a line passing through both 
poles, all the points of which have their noon contem- 



46 ARCS OF THE MERIDIAN. SECT. VI. 

poraneously. Were the lengths and curvatures of dif- 
ferent meridians known, the figure of the earth might 
be determined. But the length of one degree is suffi- 
cient to give the figure of the earth, if it be measured 
on different meridians, and in a variety of latitudes. For 
if the earth were a sphere, all degrees would be of the 
same length ; but if not, the lengths of the degrees 
would be greater, exactly in proportion as the curvature 
is less. A comparison of the length of a degree in dif- 
ferent parts of the earth's surface, will therefore deter- 
mine its size and form. 

An arc of the meridian may be measured by observ- 
ing the latitude of its extreme points (N. 124), and then 
measuring the distance between them in feet or fath- 
oms. The distance thus determined on the surface of 
the earth, divided by the degrees and parts of a degree 
contained in the difference of the latitudes, will give the 
exact length of one degree, the difference of the lati- 
tudes being the angle contained between the verticals 
at the extremities of the arc. This would be easily ac- 
complished were the distance unobstructed, and on a 
level with the sea. But, on account of the innumerable 
obstacles on the surface of the earth, it is necessary to 
connect the extreme points of the arc by a series of tri- 
angles (N. 125), the sides and angles of which are either 
measured or computed, so that the length of the arc is 
ascertained with much laborious calculation. In conse- 
quence of the irregularities of the surface, each triangle 
is in a different plane. They must therefore be reduced 
by computation to what they would have been had they 
been measured on the surface of the sea. And as the 
earth may in this case be esteemed spherical, they re- 
quire a correction to reduce them to spherical triangles. 
The gentlemen who conducted the trigonometrical sur- 
vey, in measuring 500 feet of a base in Ireland twice 
over, found that the difference in the two measurements 
did not amount to the 800th part of an inch. Such is 
the accuracy with which these operations are conduct- 
ed, and which they require. 

Arcs of the meridian have been measured in a variety 
of latitudes north and south, as well as arcs perpendicu- 
lar to the meridian. From these measurements it ap- 



SECT. VI. FORM OF EARTH FROM PENDULUM. 47 

pears that the length of the degrees increases from the 
equator to the poles, nearly in proportion to the square 
of the sine of the latitude (N. 126). Consequently, the 
convexity of the earth diminishes from the equator to 
the poles. 

Were the earth an ellipsoid of revolution, the merid- 
ians would be ellipses whose lesser axes would coincide 
with the axis of rotation, and all the degrees measured 
between the pole and the equator would give the same 
compression when combined two and two. That, how- 
ever, is far from being the case. Scarcely any of the 
measurements give exactly the same results, chiefly on 
account of local attractions, which cause the plumb line 
to deviate from the vertical. The vicinity of mountains 
has that effect. But one of the most remarkable, though 
not unprecedented, anomalies takes place in the plains of 
the north of Italy, where the action of some dense sub- 
terraneous matter causes the plumb-line to deviate seven 
or eight times more than it did from the attraction of 
Chimborazo, in the experiments of Bouguer, while 
measuring a degree of the meridian at the equator. In 
consequence of this local attraction, the degrees of the 
meridian in that part of Italy seem to increase toward 
the equator through a small space, instead of decreasing, 
as if the earth was drawn out at the poles, instead of 
being flattened. 

Many other discrepancies occur, but from the mean 
of the five principal measurements of arcs in Peru, India, 
France, England, and Lapland, Mr. Ivory has deduced 
that the figure which most nearly follows this law is an 
ellipsoid of revolution whose equatorial radius is 3962-824 
miles, and the polar radius 3949-585 miles. The differ- 
ence, or 13-239 miles, divided by the equatorial radius, 
is -i-g. nearly. This fraction is called the compression 
of the earth, and does not differ much from that given 
by the lunar inequalities. If we assume the earth to 
be a sphere, the length of a degree of the meridian is 
69J^ British miles. Therefore 360 degrees, or the 
whole circumference of the globe, is 24,856 miles, and 
the diameter, which is something less than a third of 
the circumference, is about 7916, or 8000 miles nearly. 
Eratosthenes, who died 194 years before the Christian 



48 FORM OP THE EARTH. SECT. VI. 

era, was .the first to give an approximate value ->f the 
earth's circumference, by the measurement of an arc 
between Alexandria and Syene. 

There is another method of finding the figure of the 
earth, totally different from the preceding, solely depend- 
ing upon the increase of gravitation from the equator to 
the poles. The force of gravitation at any place is 
measured by the descent of a heavy body during the first 
second of its fall. And the intensity of the centrifugal 
force is measured by the deflection of any point from the 
tangent in a second. For, since the centrifugal force bal- 
ances the attraction of the earth, it is an exact measure of 
the gravitating force. Were the attraction to cease, a body 
on the surface of the earth would fly off in the tangent 
by the centrifugal force, instead of bending round in the 
circle of rotation. Therefore, the deflection of the cir- 
cle from the tangent in a second measures the intensity 
of the earth's attraction, and is equal to the versed sine 
of the arc described during that time, a quantity easily 
determined from the known velocity of the earth's rota- 
tion. Whence it has been found, that at the equator 
the centrifugal force is equal to the 289th part of gravity. 
Now, it is proved by analysis that whatever the consti- 
tution of the earth and planets may be, if the intensity 
of gravitation at the equator be taken equal to unity, the 
sum of the compression of^the ellipsoid, and the whole 
increase of gravitation from the equator to the pole, is 
equal to five halves of the ratio of the centrifugal force 
to gravitation at the equator. This quantity with regard 
to the earth is 4 of -^ ? , or tiT-^- Consequently, the 
compression of the earth is equal to y-fj.-o diminished by 
the whole increase of gravitation. So that its form will 
be known, if the whole increase of gravitation from the 
equator to the pole can be determined by experiment. 
This has been accomplished by a method founded upon 
the following considerations : If the earth were a homo- 
geneous sphere without rotation, its attraction on bodies 
at its surface would be everywhere the same. If it 
be elliptical and of variable density, the force of gravity, 
theoretically, ought to increase from the equator to the 
pole, as unity plus a constant quantity multiplied into the 
square of the sine of the latitude (N. 126). But for a 



SKCT. VI. OSCILLATIONS OF PENDULUM. . 49 

spheroid in rotation, the centrifugal force varies, by the 
i\vs of mechanics, as the square of the sine of the lati- 
tude, from the equator, where it is greatest, to the pole, 
where it vanishes. And as it tends to make bodies fly 
off the surface, it diminishes the force of gravity by a 
small quantity. Hence, by gravitation, which is the dif- 
ference of these two forces, the fall of bodies ought to 
be accelerated from the equator to the poles proportion- 
ably to the square of the sine of the latitude ; and the 
weight of the same body ought to increase in that ratio. 
This is directly proved by the oscillations of the pendu- 
lum (N. 127), which, in fact, is a falling body; for if the 
faH of bodies be accelerated, the oscillations will be more 
rapid : in order, therefore, that they may always be per- 
formed in the same time, the length of the pendulum 
must be altered. By numerous and careful experi- 
ments, it is proved that a pendulum which oscillates 
86,400 times in a mean day at the equator, will do the 
same at every point of the earth's surface, if its length 
be increased progressively to the pole, as the square of 
the sine of the latitude. 

From the mean of these it appears that the whole 
decrease of gravitation from the poles to the equator is 
0-005.1449, which, subtracted from -j-f^.o' shows that 
the compression of the terrestrial spheroid is about 
_|^ _ 7 . This value has been deduced by the late Mr. 
Bally, president of the Astronomical Society, who has 
devoted much attention to this subject ; at the same 
time, it may be observed that no two sets of pendulum 
experiments give the same result, probably from local 
attractions. Therefore, the question cannot be con- 
sidered as definitively settled, though the differences 
are very small. The compression obtained by this 
method does not differ much from that given by the 
lunar inequalities, nor from the arcs in the direction of 
the meridian, and those perpendicular to it. The near 
coincidence of these three values, deduced by methods 
so entirely independent of each other, shows that the 
mutual tendencies of the centers of the celestial bodies 
to one another and the attraction of the earth for bodies 
at its surface result from the reciprocal attraction of all 
their particles. Another proof may be added. The 
4 K 



50 COMPRESSION OF THE EARTH. SECT. VI 

nutation of the earth's axis and the precession of the 
equinoxes (N. 143) are occasioned by the action of the 
sun and moon on the protuberant matter at the earth's 
equator. And although these inequalities do not give 
the absolute value of the terrestrial compression, they 
show that the fraction expressing it is comprised be- 
tween the limits T ^- and ^| . 

It might be e'xpected that the same compression 
should result from each, if the different methods of ob- 
servation could be made without error. This, however, 
is not the case ; for, after allowance has been made for 
every cause of error, such discrepancies are found, both 
in the degrees of the meridian and in the length of the 
pendulum, as show that the figure of the earth is very 
complicated. But they are so small, when compared 
with the general results, that they may be disregarded. 
The compression deduced from the mean of the whole 
appears not to differ much from * T ; that given by the 
lunar theory has the advantage of being independent of 
the irregularities of the earth's surface and of local at- 
tractions. The regularity with which the observed 
variation in the length of the pendulum follows the law 
of the square of the sine of the latitude, proves the 
strata to be elliptical, and symmetrically disposed round 
the center of gravity of the earth, which affords a strong 
presumption in favor of its original fluidity. It is re- 
markable how little influence the sea has on the varia- 
tion of the lengths of the arcs of the meridian, or on 
gravitation ; neither does it much affect the lunar ine- 
qualities, from its density being only about a fifth of the 
mean density of the earth. For, if the earth were to 
become a fluid, after being stripped of the ocean, it 
would assume the form of an ellipsoid of revolution 
whose compression is ^| ? . 7 , which differs very little 
from that determined by observation, and proves, not 
only that the density of the ocean is inconsiderable, but 
that its mean depth is very small. There may be pro- 
found cavities in the bottom of the sea, but its mean 
depth probably does not much exceed the mean height 
of the continents and islands above its level. On this 
account, immense tracts of land may be deserted or 
overwhelmed by the ocean, as appears really to have 



SCT. VII. PARALLAX. 51 

been the case, without any great change in the form of 
the terrestrial spheroid. The variation in the length of 
the pendulum was first remarked by Richter in 1672, 
while observing transits of the fixed stars across the 
meridian at Cayenne, about five degrees north of the 
equator. He found that his clock lost at the rate of 
2 m 28 s daily, which induced him TO determine the 
length of a pendulum beating seconds in that latitude ; 
and repeating the experiments on his return to Europe, 
he found the seconds' pendulum at Paris to be more 
than the twelfth of an inch longer than that at Cayenne. 
The form and size of the earth being determined, 
a standard of measure is furnished with which the di- 
mensions of the solar system may be compared. 



SECTION VII. 

Parallax Lunar Parallax found from direct Observation Solar Parallax 
deduced from the Transit of Venus Distance of the Sun from the 
Earth Annual Parallax Distance of the Fixed Stars. 

THE parallax of a celestial body is the angle under 
which the radius of the earth would be seen, if viewed 
from the center of that body ; it affords the means of 
ascertaining the distances of the sun, moon, and planets 
(N. 128). When the moon is in the horizon at the 
instant of rising or setting, suppose lines to be drawn 
from her center to the spectator and to the center of the 
earth ; these would form a right-angled triangle with 
the terrestrial radius, which is of a known length ; and 
as the parallax or angle at the moon can be measured, 
ah" the angles and one side are given ; whence the 
distance of the moon from the center of the earth may 
be computed. The parallax of an object may be found, 
if two observers under the same meridian, but at a very 
great distance from one another, observe its zenith 
distances on the same day at the time of its passage 
over the meridian. By such contemporaneous obser- 
vations at the Cape of Good Hope and at Berlin, the 
mean horizontal parallax of the moon was found to be 
3459", whence the mean distance of the moon is about 
sixty times the mean terrestrial radius, or 237,360 miles 



52 TRANSIT OF VENUS. SECT. VII 

nearly. Since the parallax is equal to the radius of the 
earth divided by the distance of the moon, it varies with 
the distance of the moon from the earth under the 
same parallel of latitude, and proves the ellipticity of the 
lunar orbit. When the moon is at her mean distance, 
it varies with the terrestrial radii, thus showing that 
the earth is not a sphere (N. 129). 

Although the method described is sufficiently accurate 
for finding the parallax of an object as near as the moon, 
it will not answer for the sun, which is so remote that 
the smallest error in observation would lead to a false 
result. But that difficulty is obviated by the transits of 
Venus. When that planet is in her nodes (N. 130), or 
within 1| of them, that is, in, or nearly in, the plane 
of the ecliptic, she is occasionally seen to pass over the 
sun like a black spot. If we could imagine that the sun 
and Venus had no parallax, the line described by the 
planet on his disc, and the duration of the transit, would 
be the same to all the inhabitants of the earth. But as 
the semi-diameter of the earth has a sensible magnitude 
when viewed from the center of the sun. the line de- 
scribed by the planet in its passage over his disc appears 
to be nearer to his center, or farther from it, according 
to the position of the observer ; so that the duration of 
the transit varies with the different points of the earth's 
surface at which it is observed (N. 131). This differ- 
ence of time, being entirely the effect of parallax, fur- 
nishes the means of computing it from the known 
motions of the earth and Venus, by the same method as 
for the eclipses of the sun. In fact, the ratio of the 
distances of Venus and the sun from the earth at the 
time of the transit are known from the theory of their 
elliptical motion. Consequently the ratio of the paral- 
laxes of these two bodies being inversely as their dis- 
tances, is given ; and as the transit gives the difference of 
the parallaxes, that of the sun is obtained. In 1769. the 
parallax of the sun was determined by observations of a 
transit of Venus made at Wardhus in Lapland, and at 
Otaheite in the South Sea. The latter observation was 
the object of Cook's first voyage. The transit lasted 
about six hours at Otaheite, and the difference in dura- 
tion at these two stations was eight minutes ; whence 



SKCT. VII. SOLAR PARALLAX. 53 

the sun's horizontal parallax was found to be 8"-72. 
But by other considerations it has been reduced by 
Professor Encke to 8"-5776 ; from which the mean 
distance of the sun appears to be about ninety-five mil- 
lions of miles. This is confirmed by an inequality in the 
motion of the moon, which depends upon the parallax of 
the sun, and which, when compared with observation, 
gives 8"- 6 for the sun's parallax. 

The parallax of Venus is determined by her transits ; 
that of Mars by direct observation, and it is found to be 
nearly double that of the sun, when the planet is in 
opposition. The distance of these two planets from 
the earth is therefore known in terrestrial radii, conse- 
quently their mean distances from the sun may be 
computed ; and as the ratios of the distances of the 
planets from the sun are known by Kepler's law, of the 
squares of the periodic times of any two planets being 
as the cubes of their mean distances from the sun, their 
absolute distances in miles are easily found (N. 132). 
This law is very remarkable, in thus uniting all the 
bodies of the system, and extending to the satellites as 
well as the planets. 

Far as the earth seems to be from the sun, Uranus is 
no less than nineteen times farther. Situate on the 
verge of the system, the sun must appear to it not 
much larger than Venus does to us. The earth cannot 
even be visible as a telescopic object to a body so re- 
mote. Yet man, the inhabitant of the earth, soars 
beyond the vast dimensions of the system to which his 
planet belongs, and assumes the diameter of its orbit 
as the base of a triangle whose apex extends to the 
stars. 

Sublime as the idea is, this assumption proves in- 
effectual, except in a very few cases ; for the apparent 
places of the fixed stars are not sensibly changed by the 
earth's annual revolution. With the aid derived from 
the refinements of modern astronomy, and of the most 
perfect instruments, a sensible parallax has been de- 
tected only in a veiy few of these remote suns, a Cen- 
tauri has a parallax of one second of space, therefore it 
is the nearest known star, and yet it is more than two 
hundred thousand times farther from us f han the sun 

K2 



54 MASSES OF THE PLANETS. SECT. VHI. 

is. At such a distance not only the terrestrial orbit 
shrinks to a point, but the whole solar system, seen in 
the focus of the most powerful telescope, might be 
eclipsed by the thickness of a spider's thread. Light, 
flying at the rate of 190,000 miles in a second, would 
take more than three years to travel over that space. 
One of the nearest stars may therefore have been 
kindled or extinguished more than three years, before 
we could have been aware of so mighty an event. But 
this distance must be small, when compared with that 
of the most remote of the bodies which are visible in 
the heavens. The fixed stars are undoubtedly luminous 
like the sun ; it is therefore probable that they are not 
nearer to one another than the sun is to the nearest of 
them. In the milky way and the other stariy nebulae, 
some of the stars that seem to us to be close to others, 
may be far behind them in the boundless depths of 
space; nay, may be rationally supposed to be situate 
many thousand times farther off. Light would there- 
fore require thousands of years to come to the earth 
from those myriads of suns of which our own is but 
"the remote companion." 



SECTION VIII. 

Masses of Planets that have no Satellites determined from their Perturba- 
tions Masses of the others obtained from the Motions of their Satellites 
Masses of the Sun, the Earth, of Jupiter, and of the Jovial System- 
Mass of the Moon Real Diameters of Planets, how obtained Size of 
Sun Densities of the Heavenly Bodies Formation of Astronomical 
Tables Requisite Data and Means of obtaining- them. 

THE masses of such planets as have no satellites, are 
known by comparing the inequalities they produce in 
the motions of the earth and of each other, determined 
theoretically, with the same inequalities given by ob- 
servation ; for the disturbing cause must necessarily 
be proportional to the effect it produces. The masses 
of the satellites themselves may also be compared with 
that of the sun by their perturbations. Thus, it is 
found, from the comparison of a vast number of observa- 
tions, with La Place's theory of Jupiter's satellites, 



VIII. MASS OP THE MOON. 55 

that the mass of the sun is no less than 65,000,000 
times greater than the least of these moons. But as 
the quantities of matter in any two primary planets are 
directly as the cubes of the mean distances at which 
their satellites revolve, and inversely as the squares of 
their periodic times (N. 133), the mass of the sun and 
of any planets which have satellites may be compared 
with the mass of the earth. In this manner it is com- 
puted that the mass of the sun is 354,936 times that 
of the earth ; whence the great perturbations of the 
moon, and the rapid motion of the perigee and nodes of 
her orbit (N. 134). Even Jupiter, the largest of the 
planets, has recently been found by Professor Airy to 
be 1048-7 times less than the sun; and, indeed, the 
mass of the whole Jovial System is not more than the 
1046-77th part of that of the sun. So that the mass of 
the satellites bears a very small proportion to that of 
their primary. The mass of the moon is determined 
from several sources from her action on the terres- 
trial equator, which occasions the nutation in the axis of 
rotation; from her horizontal parallax; from an in- 
equality she produces in the sun's longitude ; and from 
her action on the tides. The three first quantities, 
computed from theory and compared with their ob- 
served values, give her mass respectively equal to the 
T _ t ? |.-, and, -^.o- part of that of the earth, which do 
not differ much from each other. Dr. Brinkley, Bishop 
of Cloyne, has found it to be ^ from the constant of 
lunar nutation; but from the moon's action in raising 
the tides, her mass appears to be about the Jj part of 
that of the earth a value that cannot differ much from 
the truth. 

The apparent diameters of the sun, moon, and planets 
are determined by measurement ; therefore, their real 
diameters may be compared with that of the earth ; for 
the real diameter of a planet is to the real diameter of 
the earth, or 7916 miles, as the apparent diameter of 
the planet to the apparent diameter of the earth as seen 
from the planet, that is, to twice the parallax of the 
planet. According to Professor Bessel, the mean ap- 
parent diameter of the sun is 1922", and with the solar 
parallax 8"-5776, it will be found thatHhe diameter of 



56 DENSITIES OF CELESTIAL BODIES. SECT. VIII. 

the sun is about 886,877 miles. Therefore, if the cen- 
ter of the sUn were to coincide with the center of the 
earth, his volume would not only include the orbit of 
the moon, but would extend nearly as far again ; for 
the moon's mean distance from the earth is about sixty 
times the earth's mean radius, or 237,360 miles : so that 
twice the distance of the moon is 474,720 miles, which 
differs but little from the solar radius ; his equatorial 
radius is probably not much less than the major axis of 
the lunar orbit. The diameter of the moon is only 2160 
miles ; and Jupiter's diameter of 87,000 miles is very 
much less than that of the sun ; the diameter of Pallas 
does not much exceed 79 miles, so that an inhabitant of 
that planet, in one of our steam carriages, might go 
round his world in a few hours. 

The densities of bodies are proportional to their 
masses, divided by their volumes. Hence, if the sun 
and planets be assumed to be spheres, their volumes 
will be as the cubes of their diameters. Now, the ap- 
parent diameters of the sun and earth, at their mean 
distance, are 1922" and 17 //< 1552, and the mass of the 
earth is the 354,936th part of that of the sun taken as 
the unit. It follows, therefore, that the earth is nearly 
four times as dense as the sun. But the sun is so large, 
that his attractive force would cause bodies to fall 
through about 334-65 feet in a second. Consequently, 
if he were habitable by human beings, they would be 
unable to move, since their weight would be thirty times 
as great as it is here. A man of moderate size would 
weigh about two tons at the surface of the sun ; where- 
as at the surface of the four new planets he would be so 
light, that it would be impossible to stand steady, since 
he would only weigh a few pounds. The mean density 
of the earth has been recently determined with a de- 
gree of accuracy that leaves nothing farther to be de- 
sired. Since a comparison of the action of two planets 
upon a third gives the ratio of the masses of these two 
planets, it is clear that if we can compare the effect of 
the whole earth with the effect of any part of it, a com- 
parison may be instituted between the mass of the 
whole earth and the mass of that part of it. Now a 
leaden ball was weighed against the earth by comparing 



SECT. VIII. ASTRONOMICAL TABLES. 57 

the effects of each upon a pendulum ; the nearness of 
the smaller mass making it produce a sensible effect as 
compared with that of the larger : for by the laws of 
attraction the whole earth must be considered as col- 
lected in its center. By this method it has been found 
that the mean density -of the earth is 5-675 times greater 
than that of water at the temperature of 62 of Fahren- 
heit's thermometer. The late Mr. Baily, whose accu- 
racy as an experimental philosopher is acknowledged, 
was unremittingly occupied nearly four years in accom- 
plishing this very important object. All the planets and 
satellites appear to be of less density fhan the earth. 
The motion of Jupiter's satellites show that his density 
increases toward his center. Were his mass homogene- 
ous, his equatorial and polar axis would be in the ratio 
of 41 to 36, whereas they are observed to be only as 41 
to 38. The singular irregularities in the form of Sat- 
urn, and the great compression of Mars, prove the in- 
ternal structure of these two planets to be very far from 
uniform. 

Before entering on the theory of rotation, it may not 
be foreign to the subject to give some idea of the meth- 
ods of computing the places of the planets, and of form- 
ing astronomical tables. Astronomy is now divided into 
the three distinct departments of theory, observation, 
and computation. Since the problem of the three bod- 
ies can only be solved by approximation, the analytical 
astronomer determines the position of a planet in space 
by a series of corrections. Its place in its circular orbit 
is first found, then the addition or subtraction of the 
equation of the center (N. 48) to or from its mean place, 
gives its position in the ellipse. This again is corrected 
by the application of the principal periodic inequalities. 
But as these are determined for some particular position 
of the three bodies, they require to be corrected to suit 
other relative positions. This process is continued till 
the corrections become less than the errors of observa- 
tion, when it is obviously unnecessary to carry the ap- 
proximation further. The true latitude and distance of 
the planet from the sun are obtained by methods similar 
to those employed for the longitude. 

As the earth revolves equably about its axis in 24 



58 ASTRONOMICAL TABLES. SECT. VIII. 

hours, at the rate of 15 in an hour, time becomes a 
measure of angular motion and the principal element in 
astronomy, where the object is to determine the exact 
state of the heavens, and the successive changes it under- 
goes in all ages, past, present, and to come. Now the 
longitude, latitude, and distance of a planet from the 
sun, are given in terms of the time, by general analytical 
formulae. These formulae will consequently give the 
exact place of the body in the heavens, for any time as- 
sumed at pleasure, provided they can be reduced to 
numbers. But before the calculator begins his task, the 
observer must furnish the necessaiy data, which are, 
obviously, the forms of the orbits, and their positions 
with regard Jo the plane of the ecliptic (N. 57). It is 
therefore necessary to determine by observation for each 
planet, the length of the major axis of its orbit, the ec- 
centricity, the inclination of the orbit to the plane of the 
ecliptic, the longitudes of its perihelion and ascending 
node at a given time, the periodic time of the planet, 
and its longitude at any instant arbitrarily assumed, as 
an origin from whence all its subsequent and antecedent 
longitudes are estimated. Each of these quantities is 
determined from that position of the planet on which it 
has most influence. For example, the sum of the great- 
est and least distances of the planet from the sun is 
equal to the major axis of the orbit, and their difference 
is equal to twice the eccentricity. The longitude of the 
planet, when at its least distance from the sun, is the 
same with the longitude of the perihelion ; the greatest 
latitude of the planet is equal to the inclination of the 
orbit ; the longitude of the planet, when in the plane of 
the ecliptic in passing toward the north, is the longitude 
of the ascending node, and the periodic time is the in- 
terval between two consecutive passages of the planet 
through the same node, a small correction being made 
for the precession of the node, during the revolution of 
the planet (N. 135). Notwithstanding the excellence of 
instruments and the accuracy of modern observers, una- 
voidable errors of observation can only be compensated 
by finding the value of each element from the mean of 
a thousand, or even many thousands of observations. 
For as it is probable that the errors are not all in one 



Scr. VHI. CORRECTION OF ELEMENTS. 59 

direction, but that some are in excess and others in de- 
fect, they will compensate each other when combined. 

However, the values of the elements determined sep- 
arately, can only be regarded as approximate, because 
they are so connected, that the estimation of any one 
independently, will induce errors in the others. The 
eccentricity depends upon the longitude of the perihe- 
lion, the mean motion depends upon the major axis, the 
longitude of the node upon the inclination of the orbit, 
and vice versa. Consequently, the place of a planet com- 
puted with the approximate data will differ from its ob- 
served place. Then the difficulty is to ascertain what 
elements are most in fault, since the difference in ques- 
tion is the error of all ; that is obviated by finding the 
errors of some thousands of observations, and combining 
them, so as to correct the elements simultaneously, and 
to make the sum of the squares of the errors a minimum 
with regard to each element (N. 136). The method of 
accomplishing this depends upon the Theory of Proba- 
bilities ; a subject fertile in most important results in the 
various departments of science and of civil life, and quite 
indispensable in the determination of astronomical data. 
A series of observations continued for some years will 
give approximate values of the secular and periodic ine- 
qualities, which must be corrected from time to time, 
till theory and observation agree. And these again will 
give values of the masses of the bodies forming the solar 
system, which are important data in computing their 
motions. The periodic inequalities derived from a great 
number of observations are employed for the determina- 
tion of the values of the masses till such time as the 
secular inequalities shall be perfectly known, which will 
then give them with all the necessary precision. When 
all these quantities are determined in numbers, the lon- 
gitude, latitude, and distance of the planet from the 
sun are computed for stated intervals, and formed into 
tables, arranged according to the time estimated from a 
given epoch, so that the place of the body may be deter- 
mined from them by inspection alone, at any instant, for 
perhaps a thousand years before and after that epoch. 
By this tedious process, tables have been computed for 
eleven planets, besides the moon and the satellites of 



60 ASTRONOMICAL TABLES. SKCT. IX 

Jupiter. In the present state of astronomy, the masses 
and elements of the orbits are pretty well known^ so 
that the tables only require to be corrected from time 
to time, as observations become more accurate. Those 
containing the motions of Jupiter, Saturn, and Uranus, 
have already been twice constructed within the last thirty 
years. The tables of Jupiter and Saturn agree almost 
perfectly with modern observation ; those of Uranus, 
however, are already defective, probably because the 
discovery of that planet in 1781, is too recent to admit 
of much precision in the determination of its motions, 
or that possibly it may be subject to disturbances from 
some unseen planet revolving about the sun beyond the 
present boundaries of our system. If, after a lapse of 
years, the tables formed from a combination of numer- 
ous observations should be still inadequate to represent 
the motions of Uranus, the discrepancies may reveal 
the existence, nay even the mass and orbit of a body 
placed forever beyond the sphere of vision. 

The tables of Mars, Venus, Mercury, and even those 
of the sun, have been greatly improved, and still occupy 
the attention of Professor Airy and other distinguished 
astronomers. We are chiefly indebted to the German 
astronomers for tables of the four new planets, which 
are astonishingly perfect, considering that these bodies 
have not been discovered more than forty years, and a 
much longer time is requisite to develop their inequal- 
ities. 



SECTION IX. 

Rotation of the Sun and Planets Saturn's Rings Periods of the Rotation 
of the Moon and other Satellites equal to the Periods of their Revolu- 
tions Form of Lunar Spheroid Libratjon, Aspect, and Constitution of 
the Moon Rotation of Jupiter's Satellites. 

THE oblate form of several ot the planets indicates 
rotatory motion. This has been confirmed in most 
cases by tracing spots on their surface, by which their 
poles and times of rotation have been determined. The 
rotation of Mercury is unknown, on account of his prox- 
imity to the sun ; that of the new planets has not yet 



SECT. IX. ROTATION OF SUN AND PLANETS. 61 

been ascertained. The sun revolves in twenty-five days 
and ten hours about an axis which is directed toward a 
point half-way between the pole-star and Lyra, the plane 
of rotation being inclined by 7 30', or a little more than 
seven degrees, to the plane of the ecliptic ; it may there- 
fore be concluded that the sun's mass is a spheroid, 
flattened at the poles. From the rotation of the sun, 
there is every reason to believe that he has a progres- 
sive motion in space, although the direction to which he 
tends is unknown ; but, in consequence of the reaction 
of the planets, he describes a small irregular orbit about 
the center of gravity of the system, never deviating from 
his position by more than twice his own diameter, or a 
little more than seven times the distance of the moon 
from the earth. The sun and all his attendants rotate 
from west to east, on axes that remain nearly parallel 
to themselves (N. 137) in every point of their orbit, and 
with angular velocities that are sensibly uniform (N. 
138). Although the uniformity in the direction of their 
rotation is a circumstance hitherto unaccounted for in 
the economy of nature, yet, from the design and adapta- 
tion of eveiy other part to the perfection of the whole, 
a coincidence so remarkable cannot be accidental ; and 
as the revolutions of the planets and satellites are also 
from west to east, it is evident that both must have 
arisen from the primitive cause which determined the 
planetary motions. Indeed, La Place has computed 
the probability to be as four millions to one that all the 
motions of the planets, both of rotation and revolution, 
were at once imparted by an original common cause, 
but of which we know neither the nature nor the 
epoch. 

The larger planets rotate in shorter periods than the 
smaller planets and the earth. Their compression is, 
consequently, greater, and the action of the sun and of 
their satellites occasions a nutation in their axes and a 
precession of their equinoxes (N. 144) similar to that 
which obtains in the terrestrial spheroid, from the at- 
traction of the sun and moon on the prominent matter 
at the equator. Jupiter revolves in less than ten hours 
about an axis at right angles to certain dark belts, or 
bands, which always cross his equator. This rapid rota- 
F 



62 SATURN AND HIS RINGS. SECT. IX. 

tion occasions a very great compression in his form. 
His equatorial axis exceeds his polar axis by 6000 miles, 
whereas the difference in the axes of the earth is only 
about twenty-six and a half. It is an evident conse- 
quence of Kepler's law of the squares of the periodic 
times of the planets being as the cubes of the major 
axes of their orbits, that the heavenly bodies move 
slower the farther they are from the sun. In compa- 
ring the periods of the revolutions of Jupiter and Saturn 
with the times of their rotation, it appears that a year 
of Jupiter contains nearly ten thousand of his days, and 
that of Saturn about thirty thousand Saturnian days. 

The appearance of Saturn is unparalleled in the sys- 
tem of the world. He is a spheroid nearly 1000 times 
larger than the earth, surrounded by a ring even brighter 
than himself, which always remains suspended in the 
plane of his equator ; and, viewed with a very good 
telescope, it is found to consist of two concentric rings, 
divided by a dark band. The mean distance of the 
interior part of this double ring from the surface of the 
planet is about 22,240 miles ; it is no less than 33,360 
miles broad, but, by the estimation of Sir John Herschel, 
its thickness does not much exceed 300 miles, so that it 
appears like a plane. By the laws of mechanics, it is 
impossible that^this body can retain its position by the 
adhesion of its v particles alone. It must necessarily 
revolve with a velocity that will generate a centrifugal 
force sufficient to balance the attraction of Saturn! Ob- 
servation confirms the truth of these principles, showing 
that the rings rotate from west to east about the planet 
in ten hours and a half, which is nearly the time a satel- 
lite would take to revolve about Saturn at the same dis- 
tance. Their plane is inclined to the ecliptic, at an 
angle of 28 10' 44"-5 ; in consequence of this obliquity 
of position, they always appear elliptical to us, but with 
an eccentricity so variable as even to be occasionally like 
a straight line drawn across the planet. In the begin- 
ning of October, 1832, the plane of the rings passed 
through the center of the earth ; in that position they 
are only visible with very superior instruments, and 
appear like a fine line across the disc of Saturn. About 
the middle of December, in the same year, the rings 



S.CT. IX. ROTATION OF THE MOON. 63 

became visible with ordinary instruments, on account of 
their plane passing through the sun. In the end of 
April, 1833, the rings vanished a second time, and re- 
appeared in June of that year. Similar phenomena 
will occur in 1847, and generally as often as Saturn has 
the same longitude with either node of his rings. Each 
side of these rings has alternately fifteen years of sun- 
shine and fifteen years of darkness. A dark line has 
been seen in the outer ring, supposed to indicate a sub- 
division. 

It is a singular result of theory that the rings could 
not maintain their stability of rotation if they were 
everywhere of uniform thickness ; for the smallest dis- 
turbance would destroy the equilibrium, which would 
become more and more deranged, till at last they would 
be precipitated on the surface of the planet. The rings 
of Saturn must, therefore, be irregular solids of unequal 
breadth in different parts of the circumference, so that 
their centers of gravity do not coincide with the centers 
of their figures. Professor Strave has also discovered 
that the center of the ring is not concentric with the 
center of Saturn. The interval between the outer edge 
of the globe of the planet and the outer edge of the ring 
on one side is 11"'272, and on the other side the inter- 
val is 11"-390, consequently there is an eccentricity of 
the globe in the ring of 0"-215. If the rings obeyed 
different forces they would not remain in the same 
plane ; ' but the powerful attraction of Saturn always 
maintains them and his satellites in the plane of his 
equator. The rings, by their mutual action, and that 
of the sun and satellites, must oscillate about the center 
of Saturn, and produce phenomena of light and shadow 
whose periods extend to many years. According to M. 
Bessel the mass of Saturn's ring is equal to the yfy part 
of that of the planet. 

The periods of rotation of the moon and the other 
satellites are equal to the times of their revolutions ; 
consequently these bodies always turn the same face to 
their primaries. However, as the mean motion of the 
moon is subject to a secular inequality which will ulti- 
mately amount to many circumferences (N. 107), if the 
rotation of the moon were perfectly uniform and not 



64 ITERATIONS OF THE MOON SECT. IX. 

affected by the same inequalities, it would cease exactly 
to counterbalance the motion of revolution ; and the 
moon, in the course of ages, would successively and 
gradually discover every point of her surface to the 
earth. But theory proves that this never can happen ; 
for the rotation of the moon, though it does not partake 
of the periodic inequalities of her revolution, is affected 
by the same secular variations, so that her motions of 
rotation and revolution round the earth will always 
balance each other and remain equal. This circum- 
stance arises from the form of the lunar spheroid, which 
has three principal axes of different lengths at right 
angles to each other. 

The moon is flattened at her poles from her centri- 
fugal force ; therefore her polar axis is the least. The 
other two are in the plane of her equator ; but that 
directed toward the earth is the greatest (N. 139). The 
attraction of the earth, as if it had drawn out that part 
of the moon's equator, constantly brings the greatest 
axis, and, consequently, the same hemisphere, toward 
us, which makes her rotation participate in the secular 
variations of her mean motion of revolution. Even if 
the angular velocities of rotation and revolution had not 
been nicely balanced in the beginning of the moon's 
motion, the attraction of the earth would have recalled 
the greatest axis to the direction of the line joining the 
centers of the moon and earth, so that it would have 
vibrated on each side of that line in the same manner as 
a pendulum oscillates on each side of the vertical from 
the influence of gravitation. No such libration is per- 
ceptible ; and, as the smallest disturbance would make 
it evident, it is clear that, if the moon has ever been 
touched by a comet, the mass of the latter must have 
been extremely small. If it had been only the hundred 
thousandth part of that of the earth, it would have ren- 
dered the libration sensible. According to analysis, a 
similar libration exists in the motions of Jupiter's satel- 
lites, which still remains insensible to observation, and 
yet the comet of 1770 passed twice through the midst 
of them. 

The moon, it is true, is liable to librations depending 
upon the position of the. spectator. At her rising, part 



SBCT. IX. ROTATION OF JUPITER'S SATELLITES. 65 

9 

of the western edge of her disc is visible, which is in- 
visible at her setting, and the contrary takes place with 
regard to her eastern edge. There are also librations 
arising from the relative positions of the earth and 
moon in their respective orbits ; but as they are only 
optical appearances, one hemisphere will be eternally 
concealed from the earth. For the same reason, the 
earth, which must be so splendid an object to one lunar 
hemisphere, will be forever veiled from the other. On 
account of these circumstances, the remoter hemi- 
sphere of the moon has its day a fortnight long, and a 
night of the same duration, not even enlightened by a 
moon, while the favored side is illuminated by the re- 
flection of the earth during its long night. A planet 
exhibiting a surface thirteen times larger than that of 
the moon, with all the varieties of clouds, land, and 
water coming successively into view, must be a splen- 
did object to a lunar traveler in a journey to his an- 
tipodes. The great height of the lunar mountains prob- 
ably has a considerable influence on the phenomena of 
her motion, the more so as her compression is small, 
and her mass considerable. In the curve passing 
through the poles, and that diameter of the moon which 
always points to the earth, nature has furnished a per- 
manent meridian, to which the different spots on her 
surface hare been referred, and their positions are de- 
termined with as much accuracy as those of many of 
the most remarkable places on the surface of our globe. 
The distance and minuteness of Jupiter's satellites 
render it extremely difficult to ascertain their rotation. 
It was, however, accomplished by Sir William Herschel 
from their relative brightness. He observed that they 
alternately exceeded each other in brilliancy, and, by 
comparing the maxima and minima of then' illumination 
with their positions relatively to the sun and to their 
primary, he found that like the moon the time of their 
rotation is equal to the period of their revolution about 
Jupiter. Miraldi was led to the same conclusion with 
regard to the fourth satellite, from the motion of a spot 
on its surface. 

5 F3 



66 ROTATION OF THE EARTH. SECT. X. 



SECTION X. 

Rotation of the Earth invariable Decrease in the Earth's Mean Tempera- 
tureEarth originally in a State of Fusion Length of Day constant- 
Decrease of Temperature ascribed by Sir John Herschel to the Variation 
in the Eccentricity of the Terrestrial Orbit Difference in the Tempera- 
ture of the Two Hemispheres, erroneously ascribed to the Excess in the 
Length of Spring and Summer in the Southern Hemisphere ; attributed 
by Mr. Lyell to the Operation of existing Causes Three Principal Axes 
of Rotation Position of the Axis of Rotation on the Surface of the Earth 
invariable Ocean not sufficient to restore the Equilibrium of the Earth 
if deranged Its Density and Mean Depth Internal Structure of the 
Earth. 

THE rotation of the earth, which determines the length 
of the day, may be regarded as one of the most import- 
ant elements in the system of the world. It serves as 
a measure of time, and forms the standard of com- 
parison for the revolutions of the celestial bodies, which 
by their proportional increase or decrease would soon 
disclose any changes it might sustain. Theory and 
observation concur in proving that -among the innumer- 
able vicissitudes which prevail throughout creation, the 
period of the earth's diurnal rotation is immutable. 
The water of rivers, falling from a higher to a lower 
level, carries with it the velocity due to its revolution 
with the earth at a greater distance from the center ; it 
will therefore accelerate, although to an almost infinites- 
imal extent, the earth's daily rotation. The sum of all 
these increments of velocity arising from the descent of 
all the rivers on the earth's surface would in time be- 
come perceptible, did not nature by the process of evap- 
oration raise the waters back to their sources ; and thus, 
by again removing matter to a greater distance from 
the center, destroy the velocity generated by its pre- 
vious approach ; so that the descent of rivers does not 
affect the earth's rotation. Enormous masses projected 
by volcanos from the equator to the poles, and the con- 
trary, would indeed affect it, but there is no evidence of 
such convulsions. The disturbing action of the moon 
and planets, which has so powerful an effect on the 
revolution of the earth, in no way influences its rota- 
tion. The constant friction of the trade-winds on the 



SECT. X. INVARIABILITY OF ROTATION. (ft 

mountains and continents between the tropics does not 
impede its velocity, which theory even proves to be the 
same as if the sea together with the earth formed one 
solid mass. But although these circumstances be in- 
sufficient, a variation in the mean temperature would 
certainly occasion a corresponding change in the velocity 
of rotation. In the science of dynamics it is a principle 
in a system of bodies or of particles revolving about a 
fixed center, that the momentum or sum of the pro- 
ducts of the mass of each into its angular velocity and 
distance from the center is a constant quantity, if the 
system be not deranged by a foreign cause. Now since 
the number of particles in the system is the same what- 
ever its temperature may be, when their distances from 
the center are diminished then- angular velocity must 
be increased, in order that the preceding quantity may 
still remain constant. It follows then that as the primi- 
tive momentum of rotation with which the earth was 
projected into space must necessarily remain die same, 
the smallest decrease in heat by contracting the terres- 
trial spheroid would accelerate its rotation, and conse- 
quently diminish the length of the day. Notwithstand- 
ing the constant accession of heat from the sun's rays, 
geologists have been induced to believe from the fossil 
remains, that the mean temperature of the globe is de- 
creasing. 

The high temperature of mines, hot springs, and 
above all the internal fires which have produced and do 
still occasion such devastation on our planet, indicate an 
augmentation of heat toward its center. The increase 
of density corresponding to the depth and the form of 
the spheroid being what theory assigns to a fluid mass 
in rotation, concurs to induce the idea that the tempera- 
ture of the earth was originally so high as to reduce all 
the substances of which it is composed to a state of 
fusion or of vapor, and that in the course of ages it has 
cooled down to its present state ; that it is still becoming 
colder, and that it will continue to do so till the whole 
mass arrives at the temperature of the medium in 
which it is placed, or rather at a state of equilibrium 
between this temperature, the cooling power of its own 
radiation, and the heating effect of the sun's rays. . 



68 DECREASE OF TEMPERATURE. SJCCT. X. 

Previous to the formation of ice at the poles, the 
ancient lands of northern latitudes might no doubt have 
been capable of producing those tropical plants pre- 
served in the coal-measures, if indeed such plants could 
flourish without the intense light of a tropical sun. But 
even if the decreasing temperature of the earth be 
sufficient to produce the observed effects, it must be 
extremely slow in its operation ; for in consequence of 
the rotation of the earth being a measure of the periods 
of the celestial motions, it has been proved that if the 
length of the day had decreased by the three-thou- 
sandth part of a second since the observations of Hippar- 
chus two thousand years ago, it would have diminished 
the secular equation of the moon by 4"'4. It is there- 
fore beyond a doubt that the mean temperature of the 
earth cannot have sensibly varied during that time. If 
then the appearances exhibited by the strata are really 
owing to a decrease of internal temperature, it either 
shows the immense periods requisite to produce geo- 
logical changes, to which two thousand years are as 
nothing, or that the mean temperature of the earth had 
arrived at a state of equilibrium before these observa- 
tions. 

However strong the indications of the primitive 
fluidity of the earth, as there is no direct proof of it, 
the hypothesis can only be regarded as very probable. 
But one of the most profound philosophers and elegant 
writers of modern times has found in the secular varia- 
tion of the eccentricity of the terrestrial orbit an evident 
cause of decreasing temperature. That accomplished 
author, in pointing out the mutual dependencies of phe- 
nomena, says, " It is evident that the mean temperature 
of the whole surface of the globe, in so far as it is main- 
tained by the action of the sun at a higher degree than 
it would have were the sun extinguished, must depend 
on the mean quantity of the sun's rays which it re- 
ceives, or which comes to the same thing on the 
total quantity received in a given invariable time ; and 
the length of the year being unchangeable in all the 
fluctuations of the planetary system, it follows that the 
total amount of solar radiation will determine, cceteris 
paribus, the general climate of the earth. Now, it is 



SECT. X. DECREASE OF TEMPERATURE. 69 

not difficult to show that this amount is inversely pro- 
portional to the minor axis of the ellipse described by 
the earth about the sun (N. 140), regarded as slowly 
variable ; and that, therefore, the major axis remaining, 
as we know it to be constant, and the orbit being actu- 
ally in a state of approach to a circle, and consequently 
the minor axis being on the increase, the mean annual 
amount of solar radiation received by the whole earth 
must be actually on the decrease. We have therefore 
an evident real cause to account for the phenomenon." 
The limits of the variation in the eccentricity of the 
earth's orbit are unknown. But if its ellipticity has 
ever been as great as that of the orbit of Mercury or 
Pallas, the mean temperature of the earth must Jaave 
been sensibly higher than it is at present. Whether it 
was great enough to render our northern climates fit 
for the production of tropical plants, and for the resi- 
dence of the elephant and other animals now inhabitants 
of the torrid zone, it is impossible to say. 

Of the decrease in temperature of the northern 
hemisphere there is abundant evidence in the fossil 
plants discovered in very high latitudes, which could 
only have existed in a tropical climate, and which must 
have grown near the spot where they are found, from 
the delicacy of their structure and the perfect state of 
their preservation. This change of temperature has 
been erroneously ascribed to an excess in the duration 
of spring and summer in the northern hemisphere, in 
consequence of the eccentricity of the solar ellipse. 
The length of the seasons varies with the position of 
the perihelion (N. 64) of the earth's orbit for two 
reasons. On account of the eccentricity, small as it is, 
any line passing through the center of the sun divides 
the terrestrial ellipse into two unequal parts, and by the 
laws of elliptical motion the earth moves through these 
two portions with unequal velocities. The perihelion 
always lies in the smaller portion, and there the earth's 
motion is the most rapid. In the present position of 
the perihelion, spring and summer north of the equator 
exceed by about eight days the duration of the same 
seasons south of it. And 10,492 years ago the southern 
hemisphere enjoyed the advantage we now possess 



70 CAUSES AFFECTING THE TEMPERATURE. SECT. X. 

from the secular variation of the perihelion. Yet Sir 
John Herschel has shown that by this alteration neither 
hemisphere acquires any excess of light or heat above 
the other ; for although the earth is nearer to the sun 
while moving through that part of its orbit in which the 
perihelion lies than in the other part, and consequently 
receives a greater quantity of light and heat, yet as it 
moves faster it is exposed to the heat for a shorter 
time. In the other part of the orbit, on the contrary, 
the earth being farther from the sun receives fewer of 
his rays, but because its motion is slower it is exposed 
to them for a longer time. And as in both cases the 
quantity of heat and the angular velocity vary exactly in 
the same proportion, a perfect compensation takes place 
(N. 141). So that the eccentricity of the earth's orbit 
has little or no effect on the temperature corresponding 
to the difference of the seasons. 

Mr. Lyell, in his excellent work on Geology, refers 
the increased cold of the northern hemisphere to the 
operation of existing causes, with more probability than 
most theories that have been advanced in solution of 
this difficult subject. The loftiest mountains would be 
represented by a grain of sand on a globe six feet in 
diameter, and the depth of the ocean by a scratcl^ on 
its surface. Consequently the gradual elevation of a 
continent or chain of mountains above the surface of the 
ocean, or their depression below it, is no very great 
event compared with the magnitude of the earth, and 
the energy of its subterranean fires, if the same periods 
of time be admitted in the progress of geological as in 
astronomical phenomena, which the successive and va- 
rious races of extinct beings show to have been immense. 
Climate is always more intense in the interior of con- 
tinents than in islands or sea-coasts. An increase of 
land within the tropics would therefore augment the 
general heat, and an increase in the temperate and 
frigid zones would render the cold more severe. Now 
it appears that most of the European, North Asiatic, 
and North American continents and islands were raised 
from the deep after the coal-measures were formed in 
which the fossil tropical plants are found ; and a variety 
of geological facts indicate the existence of an ancient 



Sxrr. X. AXIS OP ROTATION INVARIABLE. 71 

and extensive archipelago throughout the greater part 
of the northern hemisphere. Mr. Lyell is therefore of 
opinion that the climate of these islands must have 
been sufficiently mild in consequence of the surrounding 
ocean to clothe them with tropical plants, and render 
them a fit abode for the huge animals whose fossil 
remains are so often found. That the arborescent ferns 
and the palms of these regions, carried by streams to 
the bottom of the ocean, were imbedded in the strata 
which were by degrees heaved up by the subterranean 
fires during a long succession of ages, till the greater 
part of the northern hemisphere became dry land as it 
now is, and that the consequence has been a continual 
decrease of temperature. 

It is evident from the marine shells found on the tops 
of the highest mountains and in almost every part of 
the globe, that immense continents have been elevated 
above the ocean, which must have ingulfed others. 
Such a catastrophe would be occasioned by a variation 
in the position of the axis of rotation on the surface of 
the earth ; for the seas tending to a new equator would 
leave some portions of the globe and overwhelm others. 
Now, it is found by the laws of mechanics that in every 
body, be its form or density what it may, there are at 
least three axes at right angles to each other, round 
any one of which, if the solid begins to rotate, it will 
continue to revolve forever, provided it be not disturbed 
by a foreign cause, but that the rotation about any 
other axis will only be for an instant, and consequently 
the poles or extremities of the instantaneous axis of 
rotation would perpetually change their position on the 
surface of the body. In an ellipsoid of revolution the 
polar diameter and every diameter in the plane of the 
equator are the only permanent axes of rotation (N. 
142). Hence if the ellipsoid were to begin to revolve 
about any diameter between the pole and the equator, 
the motion would be so unstable that the axis of rota- 
tion and the position of the poles would change every 
instant. Therefore as the earth does not differ much 
from this figure, if it did not turn round one of its prin- 
cipal axes, the position of the poles would change daily ; 
the equator, which is 90 distant, would undergo cor- 



72 AXIS OF ROTATION INVARIABLE. Sfccr. X. 

responding variations ; and the geographical latitudes of 
all places being estimated from the equator, assumed to 
be fixed, would be perpetually changing. A displace- 
ment in the position of the poles of only two hundred 
miles would be sufficient to produce these effects, and 
would immediately be detected. But as the latitudes 
are found to be invariable, it may be concluded that the 
terrestrial spheroid must have revolved about the same 
axis for ages. The earth and planets differ so little 
from ellipsoids of revolution, that in all probability any 
libration from one axis to another produced by the 
primitive impulse which put them in motion, must have 
ceased soon after their creation from the friction of the 
fluids at their surface. 

Theory also proves that neither nutation, precession, 
nor any of the disturbing forces that affect the system, 
have the smallest influence on the axis of rotation, which 
maintains a permanent position on the surface, if the 
earth be not disturbed in its rotation by a foreign cause, 
as the collision of a comet, which might have happened 
in the immensity of time. But had that been the case, 
its effects would still have been perceptible in .the varia- 
tions of the geographical latitudes. If we suppose that 
such an event had taken place, and that the disturbance 
had been very great, equilibrium could then only have 
been restored with regard to a new axis of rotation by 
the rushing of the seas to the new equator, which they 
must have continued to do till the surface was every- 
where perpendicular to the direction of gravity. But it 
is probable that such an accumulation of the waters 
would not be sufficient to restore equilibrium if the de- 
rangement had been great, for the mean density of the 
sea is only about a fifth part of the mean density of the 
earth, and the mean depth of the Pacific Ocean is sup- 
posed not to be more than four or five miles, whereas 
the equatorial diameter of the earth exceeds the polar 
diameter by about 26i miles. Consequently the influ- 
ence of the sea on the direction of gravity is veiy small. 
And as it thus appears that a great change in the posi- 
tion of the axis is incompatible with the law of equilib- 
rium, the geological phenomena in question must be 
ascribed to an internal cause. Indeed it is now demon- 



Scr. X. INTERNAL DENSITY OF THE EARTH. 73 

strated that the strata containing marine diluvia which 
are in lofty situations, must have been formed at the 
bottom of the ocean and afterward upheaved by the 
action of subterraneous fires. Besides, it is clear from 
the mensuration of the arcs of the meridian and the 
length of the seconds' pendulum, as well as from the 
lunar theory, that the internal strata and also the exter- 
nal outline of the globe are elliptical, their centers being 
coincident and their axes identical with that of the sur- 
face a state of things which, according to the distin- 
guished author lately quoted, is incompatible with a 
subsequent accommodation of the surface to a new and 
different state of rotation from that which determined 
the original distribution of the component matter. Thus 
amid the mighty revolutions which have swept innumer- 
able races of organized beings from the earth, which 
have elevated plains and buried mountains in the ocean, 
the rotation of the earth and the position of the axis on 
its surface have undergone but slight variations. 

The strata of the terrestrial spheroid are not only 
concentric and elliptical, but the lunar inequalities show 
that they increase in density from the surface of the 
earth to its center. This would certainly have happened 
if the earth had originally been fluid, for the denser parts 
must have subsided toward the center as it approached 
a state of equilibrium. But the enormous pressure of 
the superincumbent mass is a sufficient cause for the 
phenomenon. Professor Leslie observes that air com- 
pressed into the fiftieth part of its volume has its elas- 
ticity fifty times augmented. If it continues to contract 
at that rate, it would, from its own incumbent weight, 
acquire the density of water at the depth of thirty-four 
miles. But water itself would have its density doubled 
at the depth of ninety-three miles, and would even at- 
tain the density of quicksilver at a depth of 362 miles. 
Descending therefore toward the center through nearly 
4000 miles, the condensation of ordinary substances 
would surpass the utmost powers of conception. Dr. 
Young says that steel would be compressed into one- 
fourth and stone into one-eighth of its bjilk at the earth's 
center. However, we are yet ignorant of the laws of 
compression of solid bodies beyond a Certain limit ; from 
G 



74 PRECESSION. SECT. XI. 

the experiments of Mr. Perkins they appear to be ca- 
pable of a greater degree of compression than has gen- 
erally been imagined. 

But a density so extreme is not borne out by astro- 
nomical observation. It might seem to follow, there- 
fore, that our planet must have a widely cavernous 
structure, and that we tread on a crust or shell whose 
thickness bears a very small proportion to the diameter 
of its sphere. Possibly, too, this great condensation at 
the central regions may be counterbalanced by the in- 
creased elasticity due to a very elevated temperature. 



SECTION XI. 

Precession and Nutation Their Effects on the Apparent Places of the 
Fixed Stars. 

IT has been shown that the axis of rotation is invari- 
able on the surface of the earth ; and observation as well 
as theory prove that were it not for the action of the 
sun and moon on the matter at the equator, it would 
remain exactly parallel to itself in every point of its orbit. 

The attraction of an external body not only draws a 
spheroid toward it, but as the force varies inversely as 
the square of the distance, it gives it a motion about its 
center of gravity, unless when the attracting body is sit- 
uated in the prolongation of one of the axes of the sphe- 
roid. The plane of the equator is inclined to the plane 
of the ecliptic at an angle of 23 27' 34"-69 ; and the 
inclination of the lunar orbit to the same is 5 8' 4 1"' 9. 
Consequently, from the oblate figure of the earth, the 
sun and moon acting obliquely and unequally on the dif- 
ferent parts of the terrestrial spheroid, urge the plane 
of the equator from its direction and force it to move 
from east to west, so that the equinoctial points have a 
slow retrograde motion on the plane of the ecliptic, of 
50"-41 annually. The direct tendency of this action is 
to make the planes of the equator and ecliptic coincide, 
but it is balanced by the tendency of the earth to return 
to stable rotation about the polar diameter, which is one 
of its principal axes of rotation. Therefore the inclina- 



SCT. XI. PRECESSION. 75 

tion of the two planes remains constant, as a top spin- 
ning preserves the same inclination to the plane of the 
horizon. Were the earth spherical, this effect would 
not be produced, and the equinoxes would always cor- 
respond with the same points of the ecliptic, at least as 
far as this kind of motion is concerned. But another 
and totally different cause which operates on this motion 
has already been mentioned. The action of the planets 
on one another and on the sun occasions a very slow va- 
riation in the position of the plane of the ecliptic, which 
uffects its inclination to the plane of the equator, and 
gives the equinoctial points a slow but direct motion on 
the ecliptic of 0"-31 annually, which is entirely inde- 
pendent of the figure of the earth, and would be the 
same if it were a sphere. Thus the sun and moon, by 
moving the plane of the equator, cause the equinoctial 
points to retrograde on the ecliptic ; and the planets by 
moving the plane of the ecliptic give them a direct mo- 
tion, though much less than the former. Consequently 
the difference of the two is the mean precession, which 
is proved both by theory and observation to be about 
50"-1 annually (N. 143). 

As the longitudes of all the fixed stars are increased 
by this quantity, the effects of precession are soon de- 
tected. It was accordingly discovered by Hipparchus 
in the year 128 before Christ, from a comparison of his 
own observations with those of Timocharis 155 years 
before. In the time of Hipparchus, the entrance of the 
sun into the constellation Aries was the beginning of 
spring, but since that time the equinoctial points have 
receded 30, so that the constellations called the signs 
of the zodiac are now at a considerable distance from 
those divisions of the ecliptic which bear their names. 
Moving at the rate of 50"- 1 annually, the equinoctial 
points will accomplish a revolution in 25,868 years. 
But as the precession varies in different centuries the 
extent of this period will be slightly modified. Since 
the motion of the sun is direct, and that of the equinoc- 
tial points retrograde, he takes a shorter time to return 
to the equator than to arrive at the same stars ; so that 
the tropical year of 365 d 5 h 48 m 49 8 '7 must be increased 
by the time he takes to move through an arc of 50"- 1, 



76 LENGTH OF THE YEAR. SECT. XI. 

in order to have the length of the sidereal year. The 
time required is 20 m 19 s - 6, so that the sidereal year con- 
tains 365 d 6 h 9 m 9 8 -6 mean solar days. 

The mean annual precession is subject to a secular 
variation ; for although the change in the plane of the 
ecliptic in which the orbit of the sun lies be independent 
of the form of the earth, yet by bringing the sun, moon, 
and earth into different relative positions from age to 
age, it alters the direct action of the .two first on the 
prominent matter at the equator : on this account the 
motion of the equinox is greater, by 0"-455 now than it 
was in the time of Hipparchus. Consequently the ac- 
tual length of the tropical year is about 4 S> 21 shorter 
than it was at that time. The utmost change that it 
can experience from this cause amounts to 43 seconds. 

Such is the secular motion of the equinoxes. But it 
is sometimes increased and sometimes diminished by 
periodic variations, whose periods depend upon the 
relative positions of the sun and moon with regard to 
the earth, and which are occasioned by the direct ac- 
tion of these bodies on the equator. Dr. Bradley discov- 
ered that by this action the moon causes the pole of the 
equator to describe a small ellipse in the heavens, the 
axes of which are 18"-5 and 13"-674, the longer being 
directed toward the pole of the ecliptic. The period 
of this inequality is about 19 years, the time employed 
by the nodes of the lunar orbit to accomplish a revolu- 
tion. The sun causes a small variation in the descrip- 
tion of this ellipse ; it runs through its period in half a 
year. Since the whole earth obeys these motions they 
affect the position of its axis of rotation with regard to 
the starry heavens, though not with regard to the sur- 
face of the earth; for in consequence of precession 
alone the pole of the equator moves in a circle round 
the pole of the ecliptic in 25,868 years, and by nutation 
alone it describes a small ellipse in the heavens every 
19 years, on each side of which it deviates every half 
year from the action of the sun. The real curve traced 
in the starry heavens by the imaginary prolongation of 
the earth's axis is compounded of these three motions 
(N. 144). This nutatiou in the earth's axis affects both 
tho precession and obliquity with small periodic varia- 



SECT. XH. EFFECTS OF NUTATION. 77 

tions. But in consequence of the secular variation in 
the position of the terrestrial orbit, which is chiefly 
owing to the disturbing energy of Jupiter on the earth, 
the obliquity of the ecliptic is annually diminished, ac- 
cording to M. Bessel, by 0"-457. This variation in the 
course of ages may amount to 10 or 11 degrees ; but the 
obliquity of the ecliptic to 4he equator can never vary 
more than 2 42' or 3, since the equator will follow in 
some measure the motion of the ecliptic. 

It is evident that the places of all the celestial bodies 
are affected by precession and nutation. Their longi- 
tudes estimated from the equinox are augmented by 
precession ; but as it effects all the bodies equally, it 
makes no change in their relative positions. Both the 
celestial latitudes and longitudes are altered to a small 
degree by nutation ; hence all observations must be 
corrected for these inequalities. In consequence of this 
real motion in the earth's axis the pole star, forming 
part of the constellation of the Little Bear, which was 
formerly 12 from the celestial pole, is now within 1 24' 
of it, and will continue to approach it till it is within , 
after which it will retreat from the pole for ages; and 
12,934 years hence the star a Lyrae will come within 
5 of the celestial pole, and become the polar star of 
the northern hemisphere. 



SECTION XII. 

Mfean and Apparent Sidereal Time Mean and Apparent Solar Time 
Equation of Time English and French Subdivisions of Time Leap 
Year Christian Era Equinoctial Time Remarkable Eras depending 
upon the Position of the Solar Perigee Inequality of the Lengths of 
the Seasons in the two Hemispheres Application of Astronomy to Chro- 
nology English and French Standards of Weights and Measures. 

ASTRONOMY has been of immediate and essential use 
in affording invariable standards for measuring duration, 
distance, magnitude, and velocity. The mean sidereal 
day measured by the time elapsed between two consec- 
utive transits of any star at the same meridian, and the 
mean sidereal year, which is the time included between 
two consecutive returns of the sun to the same star, 
are immutable units with which all great periods of 
02 



78 SOLAR TIME. SECT. XII. 

time are compared ; the oscillations of the isochronous 
pendulum measure its smaller portions. By these in- 
variable standards alone we can judge of the slow 
changes that other elements of the system may have 
undergone. Apparent sidereal time, which is measured 
by the transit of the equinoctial point at the meridian of 
any place, is a variable quantity, from the effects of 
precession and nutation. Clocks showing apparent 
sidereal time are employed for observation, and are so 
regulated that they indicate O h O m s at the instant the 
equinoctial point passes the meridian of the observatory. 
And as time is a measure of angular motion, the clock 
gives the distances of the heavenly bodies from the 
equinox by observing the instant at which each passes 
the meridian, and converting the interval into arcs at the 
rate of 15 to an hour. 

The returns of the sun to the meridian and to the 
same equinox or solstice, have been universally adopted 
as the measure of our civil days and years. The solar 
or astronomical day is the time that elapses between 
two consecutive noons or midnights. It is consequently 
longer than the sidereal day, on account of the proper 
motion of the sun during a revolution of the celestial 
sphere. But as the sun moves with greater rapidity at 
the winter than at the summer solstice, the astronomi- 
cal day is more nearly equal to the sidereal day in sum- 
mer than in winter. The obliquity of the ecliptic also 
affects its duration ; for near the equinoxes the arc of 
the equator is less than the corresponding arc of the 
ecliptic, and in the solstices it is greater (N. 145). The 
astronomical day is therefore diminished in the first 
case, and increased in the second. If the sun moved 
uniformly in the equator at the rate of 59' 8"- 33 every 
day, the solar days would be all equal. The time there- 
fore which is reckoned by the arrival of an imaginary 
sun at the meridian, or of one which is supposed to 
move uniformly in the equator, is denominated mean 
solar time, such as is given by clocks and watches in 
common life. When it is reckoned by the arrival of the 
real sun at the meridian it is apparent time, such as is 
given by dials. The difference between the time shown 
by a clock and a dial is the equation of time given in 



SICT. XII. DIVISIONS OF TIME. 79 

the Nautical Almanac, sometimes amounting to as much 
as sixteen minutes. The apparent and mean time coin- 
cide four times in the year ; when the sun's daily mo- 
tion in right ascension is equal to 59' &" 33 in a mean 
solar day, which happens about the 16th of April, the 
16th of June, the 1st of September, and the 25th of 
December. 

The astronomical day begins at noon, but in common 
reckoning the day begins at midnight. In England it is 
divided into twenty-four hours, which are counted by 
twelve and twelve ; but in France astronomers, adopting 
the decimal division, divide the day into ten hours, the 
hour into one hundred minutes, and the minute into a 
hundred seconds, because of the facility in computation, 
and in conformity with then* decimal system of weights 
and measures. This subdivision is not now used in 
common life, nor has it been adopted in any other 
country ; and although some scientific writers in France 
still employ that division of time, the custom is begin- 
ning to wear out. At one period during the French 
revolution, the clock in the gardens of the Tuileries was 
regulated to show decimal time. The mean length of 
the day, though accurately determined, is not sufficient 
for the purposes either of astronomy or civil life. The 
tropical or civil year of 365 d 5 U 48 m 49 8 -7, which is the 
time elapsed between the consecutive returns of theun 
to the mean equinoxes or solstices, including all the 
changes of the seasons, is a natural cycle peculiarly 
suited for a measure of duration. It is estimated from 
the winter solstice, the middle of the long annual night 
under the north pole. But although the length of the 
civil year is pointed out by nature as a measure of long 
periods, the incommensurability that exists between the 
length of the day and the revolution of the sun, renders 
it difficult to adjust the estimation of both in whole num- 
bers. If the revolution of the sun were accomplished 
in 365 days, all the years would be of precisely the same 
number of days, and would begin and end with the sun 
at the same point of the ecliptic. But as the sun's revo- 
lution includes the fraction of a day, a civil year and a 
revolution of the sun have not the same duration. Since 
the fraction is nearly the fourth of a day, in four years 



80 LENGTH OF THE CIVIL YEAR. SECT. XII. 

it is nearly equal to a revolution of the sun, so that the 
addition of a supernumerary day every fourth year 
nearly compensates the difference. But in process of 
time further correction will be necessary, because the 
fraction is less than the fourth of a day. In fact, if a 
bissextile be suppressed at the end of three out of four 
centuries, the year so determined will only exceed the 
true year by an extremely small fraction of a day ; and 
if in addition to this a bissextile be suppressed every 
4000 years, the length of the year will be nearly equal 
to that given by observation. Were the fraction neg- 
lected, the beginning of the year would precede that of 
the tropical year, so that it would retrograde through 
the different seasons in a period of about 1507 years. 
The Egyptian year began with the heliacal rising of 
Sirius, and contained only 365 days, by which they lost 
one year in every 1461 years, their Sothaic period, or that 
cycle in which the heliacal rising of Sirius passes through 
the whole year and takes place again on the same day. 
The commencement of that cycle is placed by ancient 
chronologists in the year 1322 before the Christian era. 
The division of the year into months is very old and almost 
universal. But the period of seven days, by far the 
most permanent division of time, and the most ancient 
monument of astronomical knowledge, was used by the 
Brahmins in India with the same denominations em- 
ployed by us, and was alike found in the calendars of the 
Jews, Egyptians, Arabs, and Assyrians. It has survived 
the fall of empires, and has existed among all successive 
generations, a proof of their common origin. 

The day of the new moon immediately following the 
winter solstice in the 707th year of Rome, was made the 
1st of January of the first year of Julius Caesar. The 
25th of December of his forty-fifth year is considered as 
the date of Christ's nativity ; and the forty-sixth year of 
the Julian Calendar is assumed to be the first of our 
era. The preceding year is called the first year before 
Christ by chronologists, but by astronomers it is called 
the year 0. The astronomical year begins on the 31st 
of December at noon ; and the date of an observation 
expresses the days and hours which have actually elapsed 
since that time. 



SCT. XII. ASTRONOMICAL ERAS. 81 

. Since solar and sidereal time are estimated from the 
passage of the sun and the equinoctial point across the 
meridian of each place, the hours are different at differ- 
ent places : while it is one o'clock at one place it is two 
at another, three at another, &c. ; for it* is obvious that 
it is noon at one part of the globe, at the same moment 
that it is midnight at another diametrically opposite to it; 
consequently an event which happens at one and the 
same instant of absolute time is recorded at different 
places, as having happened at different times. There- 
fore, when observations made at different places are to 
be compared, they must be reduced by computation to 
what they would have been had they been made under 
the same meridian. To obviate this, it was proposed by 
Sir John Herschel to employ mean equinoctial time, 
which is the same for all the world, and independent 
alike of local circumstances and inequalities in the sun's 
motion. It is the time elapsed from the instant the mean 
sun enters the mean vernal equinox, and is reckoned in 
mean solar days and parts of a day. 

Some remarkable astronomical eras are determined by 
the position of the major axis of the solar ellipse, which 
depends upon the direct motion of the perigee (N. 102) 
and the precession of the equinoxes conjointly, the 
annual motion of the one being ]1"*8, and that of the 
other 50"-1. Hence the axis, moving at the rate of 
61"-9 annually, accomplishes a tropical revolution in 
209-84 years. It coincided with the line of the equinoxes 
4000 or 4089 years before the Christian era, much about 
the time chronologists assign for the creation of man. In 
6483 the major axis will again coincide with the line of 
the equinoxes ; but then the solar perigee will coincide 
with the equinox of autumn ; whereas at the creation of 
man it coincided with the vernal equinox. In the year 
1246 the major axis was perpendicular to the line of the 
equinoxes ; then the solar perigee coincided with the 
solstice of summer, and the apogee with the solstice of 
winter. According to La Place, who computed these 
periods from different data, the last coincidence hap- 
pened in the year 1250 of our era, which induced him to 
propose that year as a universal epoch, the vernal equi- 
nox of the year 1250 to be the first day of the first year. 
6 



82 ANCIENT CHRONOLOGY. SECT. XII 

These eras can only be regarded as approximate, since 
ancient observations are too inaccurate, and modern ob- 
servations too recent, to afford data for their precise 
determination. 

The variation in the position of the solar ellipse occa- 
sions corresponding changes in the length of the seasons. 
In its present position spring is shorter than summer, 
and autumn longer than winter ; and while the solar 
perigee continues as it now is between the solstice of 
winter and the equinox of spring, the period including 
spring and summer will be longer than that including 
autumn and winter. In this century the difference is 
between seven and eight days. The intervals will be 
equal toward the year 6483, when the perigee will coin- 
cide with the equinox of spring ; but when it passes that 
point, the spring and summer taken together will be 
shorter than the period including the autumn and winter 
(N. 147). These changes will be accomplished in a 
tropical revolution of the major axis of the earth's orbit, 
which includes an interval of 20,984 years. Were the 
orbit circular, the seasons would be equal ; their differ- 
ence arises from the eccentricity of the orbit, small as it 
is ; but the changes are so trifling as to be imperceptible 
in the short span of human life. 

No circumstance in the whole science of astronomy 
excites a deeper interest than its application to chronol- 
ogy. "Whole nations," says La Place, "have been 
swept from the earth, with their languages, arts, and 
sciences, leaving but confused masses of ruins to mark 
the place where mighty cities stood ; their history with 
the exception of a few doubtful traditions has perished ; 
but the perfection of their astronomical observations 
marks their high antiquity, fixes the periods of their ex- 
istence, and proves that even at that early time they 
must have made considerable progress in science." The 
ancient state of the heavens may now be computed with 
great accuracy ; and by comparing the results of calcu- 
lation with ancient observations, the exact period at 
which they were made may be verified if true, or if 
false their error may be detected. If the date be accu- 
rate and the observation good, it will verify the accuracy 
of modern tables, and will show to how many centuries 



SECT. XII. ANCIRNT ASTRONOMY. 83 

they may be extended without the fear of error. A few 
examples will show the importance of the subject. 

At the solstices the sun is at his greatest distance from 
the equator, consequently his declination at these times 
is equal to the obliquity of the ecliptic (N. 148), which 
was formerly determined from the meridian length of 
the shadow of the stile of a dial on the day of a solstice. 
The lengths of the meridian shadow at the summer and 
winter solstices are recorded to have been observed at 
the city of Layang, in China, 1100 years before the 
Christian era. From these the distances of the sun 
from the zenith (N. 149) of the city of Layang are 
known. Half the sum of these zenith distances de- 
termines the latitude, and half their difference gives the 
obliquity of the ecliptic at the period of the observation ; 
and as the law of the variation of the obliquiryis known, 
both the time and place of the observations have been 
verified by computations from modern tables. Thus 
the Chinese had made some advances in the science of 
astronomy at that early period. Their whole chronol- 
ogy is founded on the observations of eclipses, which 
prove the existence of that empire for more than 4700 
years. The epoch of the lunar tables of the Indians, 
supposed by Bailly to be 3000 years before the Chris- 
tian era, was proved by La Place, from the acceleration 
of the moon, not to be more ancient than the time of 
Ptolemy, who lived in the second century after it. The 
great inequality of Jupiter and Saturn, whose cycle em- 
braces 918 years, is peculiarly fitted for marking the 
civilization of a people. The Indians had determined 
the mean motions of these two planets in that part of 
their periods, when the apparent mean motion of Saturn 
was at the slowest, and that of Jupiter the most rapid. 
The periods in which that happened were 3102 years 
before the Christian era, and the year 1491 after it. 
The returns of comets to their perihelia may possibly 
mark the present state of astronomy to future ages. 

The places of the fixed stars are affected by the pre- 
cession of the equinoxes ; and as the law of that varia- 
tion is known, their positions at any time may be com- 
puted. Now Eudoxus, a contemporary of Plato, men- 
tions a star situate in the pole of the equator, and it ap- 



84 WEIGHTS AND MEASURES. SECT. XII. 

pears from computation that K Draconis was not very 
far from that place about 3000 years ago ; but as- it is 
only about 2150 years since Eudoxus lived, he must 
have described an anterior state of the heavens, sup- 
posed to be the same that was mentioned by Chiron 
about the time of the siege of Troy. Thus every cir- 
cumstance concurs in showing that astronomy was cul- 
tivated in the highest ages of antiquity. 

It is possible that a knowledge of astronomy may lead 
to the interpretation of hieroglyphical characters. As- 
tronomical signs are often found on the ancient Egyptian 
monuments, probably employed by the priests to record 
dates. The author had occasion to witness an instance 
of this most interesting application of astronomy, in as- 
certaining the date of a papyrus, sent from Egypt by Mr. 
Salt, in the hieroglyphical researches of the late Dr. 
Thomas Young, whose profound and varied acquire- 
ments do honor to his country, and to the age in which 
he lived. The manuscript was found in a mummy case ; 
it proved to be a horoscope of the age of Ptolemy, and 
its date was determined from the configuration of the 
heavens at the time of its construction. 

The form of the earth furnishes a standard of weights 
and measures for the ordinary purposes of life, as well 
as for the determination of the masses and distances of 
the heavenly bodies. The length of the pendulum 
vibrating seconds of mean solar time in the latitude of 
London, forms the standard of the British measure of 
extension. Its approximate length oscillating in vacuo 
at the temperature of 62 of Fahrenheit, and reduced 
to the level of the sea (N. 150), was determined by 
Captain Kater to be 39-1393 inches. The weight of a 
cubic inch of water at the temperature of 62 of 
Fahrenheit, barometer 30 inches, was also determined 
in parts of the imperial troy pound, whence a standard 
both of weight and capacity was deduced. The French 
have adopted the metre equal to 3-2808992 English feet 
for their unit of linear measure, which is the ten-mil- 
lionth part of that quadrant of the meridian (N. 151), 
passing through Formentera and Greenwich, the middle 
of which is nearly in the forty-fifth degree of latitude. 
Should the national standards of the two countries be 



Scr X1H. WEIGHTS AND MEASURES 85 

lost in the vicissitude of human affairs, both may be 
recovered ; since they are derived from natural standards 
presumed to be invariable. The length of the pendu- 
lum would be found again with more facility than the 
metre. But as no measure is mathematically exact, an 
error in the original standard may at length become 
sensible in measuring a great extent, whereas the error 
that must necessarily arise in measuring the quadrant of 
the meridian is rendered totally insensible by subdi- 
vision in taking its ten-millionth part. The French 
have adopted the decimal division, not only in time but 
also in their degrees, weights, and measures, on account 
of the very great facility it affords in computation. It 
has not been adopted by any other people, though 
nothing is more desirable than that all nations should 
concur in using the same standards, not only on account 
of convenience, but as affording a more definite idea of 
quantity. It is singular that the decimal division of the 
day, of degrees, weights, and measures, was employed 
in China 4000 years ago ; and that at the time Ibn Tunis 
made his observations at Cairo about the year 1000 of 
the Christian era, the Arabs were in the habit of em- 
ploying the vibrations of the pendulum in their astro- 
nomical observations as a measure of time. 



SECTION XIII. 

Tides Forces that produce them Three kinds of Oscillations in the Ocean 
The Semidiurnal Tides Equinoctial Tides Effects of the Declina- 
tion of the Sun and Moon Theory insufficient without Observation 
Direction of the Tidal Wave Height of Tides Mass of Moon obtained 
from her Action on the Tides Interference of Undulations Impossi- 
bility of a Universal Inundation Currents. 

ONE of the most immediate and remarkable effects of 
a gravitating force external to the earth, is the alternate 
rise and fall of the surface of the sea twice in the course 
of a lunar day, or 24 h 50 m 28 s of mean solar time. As it 
depends upon the action ofthe sun and moon, it is classed 
among astronomical problems, of which it is by far the 
most difficult and its explanation the least satisfactory. 
The form of the surface of the ocean in equilibrio when 
revolving with the earth round its axis, is an ellipsoid 
H 



86 THEORY OF THE TIDES. SKCT. XIH. 

flattened at the poles ; but the action of the sun and 
moon, especially of the moon, disturbs the equilibrium of 
the ocean. If the moon attracted the center of gravity 
of the earth and all its particles with equal and parallel 
forces, the whole system of the earth and the waters 
that cover it would yield to these forces with a common 
motion, and the equilibrium of the seas would remain 
undisturbed. The difference of the forces and the ine- 
quality of their directions alone disturb the equilibrium. 

It is proved by daily experience as well as by strict 
mathematical reasoning, that if a number of waves or 
oscillations be excited in a fluid by different forces, each 
pursues its course and has its effect independently of 
the rest. Now in the tides there are three kinds of 
oscillations depending on different causes, and producing 
their effects independently of each other, which may 
therefore be estimated separately. 

The oscillations of the first kind, which are very small, 
are independent of the rotation of the earth ; and as they 
depend upon the motion of the disturbing body in its 
orbit, they are of long periods. The second kind of 
oscillations depends upon the rotation of the earth, 
therefore their period is nearly a day. The oscillations 
of the third kind vary with an angle equal to twice the 
angular rotation of the earth, and consequently happen 
twice in twenty-four hours (N. 152). The first afford 
no particular interest, and are extremely small ; but the 
difference of two consecutive tides depends upon the 
second. At the time of the solstices, this difference, 
which ought to be very great according to Newton's 
theory, is hardly sensible on our shores. La Place has 
shown that the discrepancy arises from the depth of the 
sea ; and that if the depth were uniform, there would 
be no difference in the consecutive tides but that which 
is occasioned by local circumstances. It follows there- 
fore that as this difference is extremely small, the sea 
considered in a large extent must be nearly of uniform 
depth ; that is to say, there is a certain mean depth from 
which the deviation is not great. The mean depth of 
the Pacific Ocean is supposed to be about four or five 
miles, that of the Atlantic only three or four, which, 
however, is mere conjecture. From the formula 3 , which 



SBCT. XIII. THEORY OF THE TIDES. 87 

determine the difference of the consecutive tides, it is 
proved that the precession of the equinoxes, and the 
nutation of the earth's axis, are the same as if the sea 
formed one solid mass with the earth. 

Oscillations of the third kind are the semidiurnal tides 
so remarkable on our coasts. They are occasioned by 
the combined action of the sun and moon ; but as the 
effect of each is independent of the other, they may be 
considered separately. 

The particles of water under the moon are more at- 
tracted than the center of gravity of the earth, in the 
inverse ratio of the square of the distances. Hence 
they have a tendency to leave the earth, but are retained 
by their gravitation, which is diminished by this tendency. 
On the contrary, the moon attracts the center of the 
earth, more powerfully than she attracts the particles of 
water in the hemisphere opposite to her ; so that the 
earth has a tendency to leave the waters, but is retained 
by gravitation, which is again diminished by this tendency. 
Thus the waters immediately under the moon are drawn 
from the earth, at the same time that the earth is drawn 
from those which are diametrically opposite to her, in 
both instances producing an elevation of the ocean of 
nearly the same height above the surface of equilibrium; 
for the diminution of the gravitation of the particles in 
each position is almost the same, on account of the dis- 
tance of the moon being great in comparison of the ra- 
dius of'the earth. Were the earth entirely covered by 
the sea, the waters thus attracted by the moon would 
assume the form of an oblong spheroid whose greater 
axis would point toward the moon ; since the columns of 
water under the moon, and in the direction diametrically 
opposite to her, are rendered lighter in consequence of 
the diminution of their gravitation ; and in order to pre- 
serve the equilibrium, the axes 90 distant would be 
shortened. The elevation, on account of the smaller 
space to which it is confined, is twice as great as the 
depression ; because the contents of the spheroid always 
remain the same. If the waters were capable of assum- 
ing the form of equilibrium instantaneously, that is the 
form of the spheroid, its summit would always point to 
the.inoon notwithstanding the earth's rotation. But on 



88 THE SEMIDIURNAL TIDES. SECT. XIII. 

account of their resistance, the rapid motion produced 
in them by rotation prevents them from assuming at 
every instant the form which the equilibrium of the 
forces acting upon them requires. Hence on account 
of the inertia of the waters, if the tides be considered 
relatively to the whole earth and open seas, there is a 
meridian about 30 eastward of the moon, where it is 
always high water both in the hemisphere where the 
moon is and in that which is opposite. On the west 
side of this circle the tide is flowing, on the east it is 
ebbing, and on every part of the meridian at 90 distant 
it is low water. This great wave, which follows all the 
motions of the moon as far as the rotation of the earth 
will permit, is modified by the action of the sun, the 
effects of whose attraction are in every respect like 
those produced by the J moon, though greatly less in de- 
gree. Consequently a similar wave, but much smaller, 
raised by the sun tends to follow his motions, which at 
times combines with the lunar wave, and at others op- 
poses it, according to the relative positions of the two 
luminaries ; but as the lunar wave is only modified a 
little by the solar, the tides must necessarily happen 
twice in a day, since the rotation of the earth brings the 
same point twice under the meridian of the moon in 
that time, once under the superior and once under the 
inferior meridian. 

In the semidiurnal tides there are two phenomena 
particularly to be distinguished, one occurring twice in a 
month, and the other twice in a year. 

The first phenomenon is that the tides are much in- 
creased in the syzygies, or at the time of new and full 
moon (N. 153). In both cases the sun and moon are in 
the same meridian : for when the moon is new they are 
in conjunction ; and when she is full they are in opposi- 
tion. In each of these positions, their action is com- 
bined to produce the highest or spring tides under that 
meridian, and the lowest in those points that are 90 
distant. It is observed that the higher the sea rises in 
full tide, the lower it is in the ebb. The neap tides take 
place when the moon is in quadrature ; they neither rise 
so high nor sink so low as the spring tides. The spring 
tides are much increased when the moon is in perigee, 



SCT. Xffl. SPRING AND NEAP TIDES. 89 

because she is then nearest to the earth. It is evident 
that the strong tides must happen twice in a month, 
since in that time the moon is once new and once full. 

The second phenomenon in the tides is the augmen- 
tation occurring at the time of the equinoxes when the 
sun's declination (N. 154) is zero, which happens twice 
every year. The greatest tides take place when a new 
or full moon happens near the equinoxes, while the 
moon is in perigee. The inclination of the moon's orbit 
to the ecliptic is 5 8' 47"-9; hence in the equinoxes the 
action of the moon would be increased if her node were 
to coincide with her perigee ; for it is clear that the ac- 
tion of the sun and moon on the ocean is most direct 
and intense when they are in the plane of the equator, 
and in the same meridian, and when the moon in con- 
junction or opposition is at her least distance from the 
earth. The spring tides which happen under all these 
favorable circumstances must be the greatest possible. 
The equinoctial gales often raise them to a great height. 
Besides these remarkable variations, there are others 
arising from the declination or angular distance of the 
sun and moon from the plane of the equator, which have 
a great influence on the ebb and flow of the waters. The 
sun and moon are continually making the circuit of the 
heavens at different distances from the plane of the 
equator, on account of the obliquity of the ecliptic and 
the inclination of the lunar orbit. The moon takes about 
twenty-nine days and a half to vary through all her de- 
clinations, which sometimes extend 28| degrees on each 
side of the equator, while the sun requires nearly 365| 
days to accomplish his motion from tropic to tropic 
through about 23^ degrees ; so that their combined mo- 
tion causes great irregularities, and at times their at- 
tractive forces counteract each other's effects to a certain 
extent ; but on an average the mean monthly range of 
the moon's declination is nearly the same as the annual 
range of the declination of the sun : consequently the 
highest tides take place within the tropics, and the low- 
est toward the poles. The declination of the moon 
likewise causes the two tides of the same day to rise to 
unequal heights ; this diurnal inequality of course van- 
ishes when the moon is in the equator. 
H2 



90 THEORY OP THE TIDES. SECT. XIII. 

Both the height and time of high water are thus per- 
petually changing ; therefore, in solving the problem, it 
is required to determine the heights to which the tides 
rise, the times at which they happen, and the daily vari- 
ations. Theory and observation show that each partial 
tide increases as the cube of the apparent diameter, or 
of the parallax of the body which produces it, and that it 
diminishes as the square of the cosine of the declination 
of that body (N. 154) ; for the greater the apparent di- 
ameter, the nearer the body, and the more intense its 
action on the sea; but the greater the decimation, the 
less the action, because it is less direct. 

The periodic motions of the waters of the ocean, on 
the hypothesis of an ellipsoid of revolution entirely cov- 
ered by the sea, are very far from according with obser- 
vation. This arises from the very great irregularities in 
the surface of the earth, which is but partially covered 
by the sea ; from the variety in the depths of the ocean, 
the manner in which it is spread out on the earth, the 
position and inclination of the shores, the currents, and 
the resistance the waters meet with causes impossible 
to estimate, but which modify the oscillations of the 
great mass of the ocean. However, amid all these 
irregularities, the ebb and flow of the sea maintain a 
ratio to the forces producing them sufficient to indicate 
their nature and to verify the law of the attraction of the 
sun and moon on the sea. La Place observes that the 
investigation of such relations between cause and effect 
is no less useful in natural philosophy than the direct 
solution of problems either to prove the existence of the 
causes or to trace the laws of their effects. Like the 
theory of probabilities, it is a happy supplement to the 
ignorance and weakness of the human mind. Thus 
the problem of the tides does not admit of a general 
solution. It is, indeed, necessary to analyze the general 
phenomena which ought to result from the attraction of 
the sun and moon ; but these must be corrected in each 
particular case by local observations modified by the 
extent and depth of the sea, and the peculiar circum- 
stances of the place. 

Since the disturbing action of the sun and moon can 
only become sensible in a very great extent of water, 



Scr. XIII. HEIGHT OF THE TIDES. 91 

the Pacific Ocean must be one of the principal sources 
of our tides ; but, in consequence of the rotation of the 
earth and the inertia of the ocean, high water does not 
happen till some time after the moon's southing (N. 155). 
The tide raised in that world of waters is transmitted to 
the Atlantic, from which sea it moves in a northerly 
direction along the coasts of Africa and Europe, arriving 
later and later at each place. This great wave, how- 
ever, is modified by the tide raised in the Atlantic, 
which sometimes combines with that from the Pacific 
in raising the sea, and sometimes is in opposition to it, 
so that the tides only rise in proportion to their differ- 
ence. This vast combined wave, reflected by the shores 
of the Atlantic, extending nearly from pole to pole, still 
coming northward, pours through the Irish and British 
Channels into the North Sea ; so that the tides in our 
ports are modified by those of another hemisphere. 
Thus the theory of the t&ies in each port, both as to their 
height and the times at which they take place, is really 
a matter of experiment, and can only be perfectly deter- 
mined by the mean of a very great number of observa- 
tions, including several revolutions of the moon's nodes. 
The height to which the tides rise is much greater in 
narrow channels than in the open sea, on account of the 
obstructions they meet with. The sea is so pent up in 
the British Channel that the tides sometimes rise as 
much as fifty feet at St. Malo on the coast of France ; 
whereas on the shores of some of the South Sea islands 
near the center of the Pacific they do not exceed one 
or two feet. The winds have great influence on the 
height of the tides, according as they conspire with or 
oppose them ; but the actual effect of the wind in ex- 
citing the waves of the ocean extends very little below 
the surface. Even in the most violent storms, the water 
is probably calm at the depth of ninety or a hundred 
feet. The tidal wave of the ocean does not reach the 
Mediterranean nor the Baltic, partly from their position 
and partly from the narrowness of the Straits of Gib- 
raltar and of the Categat, but it is very perceptible in 
the Red Sea and in Hudson's Bay. In high latitudes, 
where the ocean is less directly under the influence of 
the luminaries, the rise and fall of the sea w inconsider- 



92 ACTION OP SUN AND MOON. SECT. XIII. 

able, so that in all probability there is no tide at the 
poles, or only a small annual and monthly tide. The 
ebb and flow of the sea are perceptible in rivers to a 
very great distance from their estuaries. In the Straits 
of Pauxis, in the river of the Amazons, more than five 
hundred miles from the sea, the tides are evident. It 
requires so many days for the tide to ascend this mighty 
stream, that the returning tides meet a succession of 
those which are coming up ; so that every possible vari- 
ety occurs at some part or other of its shores, both as 
to magnitude and time. It requires a very wide expanse 
of water to accumulate the impulse of the sun and moon, 
so as to render their influence sensible ; on that account 
the tides in the Mediterranean and Black Sea are 
scarcely perceptible. 

These perpetual commotions in the waters are occa- 
sioned by forces that bear a very small proportion to 
terrestrial gravitation : the sun's action in raising the 
ocean is only the ^^ r VrroT f gravitation at the earth's 
surface, and the action of the moon is little more than 
twice as much ; these forces being in the ratio of 1 to 
2-35333, when the sun and moon are at their mean dis- 
tances from the earth. From this ratio the mass of the 
moon is found to be only the ^ part of that of the earth. 
Had the action of the sun on the ocean been exactly 
equal to that of the moon, there would have been no 
neap tides, and the spring tides would have been of 
twice the height which the action of either the sun or 
moon would have produced separately ; a phenomenon 
depending upon the interference of the waves or undu- 
lations. 

A stone plunged into a pool of still water occasions a 
series of waves to advance along the surface, though the 
water itself is not carried forward, but only rises into 
heights and sinks into hollows, each portion of the sur- 
face being elevated and depressed in its turn. Another 
stone of the same size thrown into the water near the 
first, will occasion a similar set of undulations. Then if 
an equal and similar wave from each stone arrive at the 
same spot at the same time, so that the elevation of the 
one exactly coincides with the elevation of the other, 
their united effect will produce a wave twice the size of 



XIIL INTERFERENCE OF WAVES. . 93 

either. But if one wave precede the other by exactly 
half an undulation, the elevation of the one will coincide 
with the hollow of the other, and the hollow of the one 
with the elevation of the other ; and the waves will so 
entirely obliterate one another, that the surface of the 
water will remain smooth and level. Hence if the length 
of each wave be represented by 1, they will destroy one 
another at intervals of , , 4, &c., and will combine 
their effects at the intervals 1, 2, 3, &c. It will be found 
according to this principle, when still water is disturbed 
by the fall of two equal stones, that there are certain 
lines on its surface of a hyperbolic form, where the 
water is smooth in consequence of the waves oblitera- 
ting each other ; and that the elevation of the water in 
the adjacent parts corresponds to both the waves united 
(N. 156). Now in the spring and neap tides arising 
from the combination of the simple soli-lunar waves, the 
spring tide is the joint result of the combination when 
they coincide in time and place ; and the neap tide hap- 
pens when they succeed each other by half an interval, 
so as to leave only the effect of their difference sensible. 
It is therefore evident that if the solar and lunar tides 
were of the same height, there would be no difference, 
consequently no neap tides, and the spring tides would 
be twice as high as either separately. In the port of 
Batsha in Tonquin, where the tides arrive by two chan- 
nels of lengths corresponding to half an interval, there 
is neither high nor low water, on account of the inter- 
ference of the waves. 

The initial state of the ocean has no influence on the 
tides; for whatever its primitive conditions may have 
been, they must soon have vanished by the friction and 
mobility of the fluid. One of the most remarkable cir- 
cumstances in the theory of the tides is the assurance, 
that in consequence of the density of the sea being only 
one-fifth of the mean density of the earth, and the earth 
itself increasing in density toward the center, the sta- 
bility of the equilibrium of the ocean never can be sub- 
verted by any physical cause. A general inundation 
arising from the mere instability of the ocean is there- 
fore impossible. A variety of circumstances however 
tend to produce partial variations in the equilibrium of 



94 CURRENTS IN THE OCEAN. SECT. XIII. 

the seas, which is restored by means of currents. Winds 
and the periodical melting of the ice at the poles occa- 
sion temporary water-courses ; but by far the most im- 
portant causes are the centrifugal force induced by the 
velocity of the earth's rotation, and variations in the 
density of the sea. 

The centrifugal force may be resolved into two forces 
one perpendicular, and another tangent to the earth's 
surface (N. 157). The tangential force, though small, 
is sufficient to make the fluid particles within the polar 
circles tend toward the equator, and the tendency is 
much increased by the immense evaporation in the 
equatorial regions from the heat of the sun, which dis- 
turbs the equilibrium of the ocean. To this may also 
be added the superior density of the waters near the 
poles, partly from their low temperature and partly 
from their gravitation being less diminished by the ac- 
tion of the sun and moon than that of the seas of lower 
latitudes. In consequence of the combination of all 
these circumstances, two great currents perpetually set 
from each pole toward the equator. But as they come 
from latitudes where the rotatory motion of the surface 
of the earth is very much less than it is between the 
tropics, on account of their inertia, they do not im- 
mediately acquire the velocity with which the solid part 
of the earth's surface is revolving at the equatorial re- 
gions ; from whence it follows that within twenty-five 
or thirty degrees on each side of the line, the ocean 
appears to have a general motion from east to west, 
which is much increased by the action of the trade 
winds. This mighty mass of rushing waters at about 
the tenth degree of south latitude is turned toward the 
north-west by the coast of America, runs through the 
Gulf of Mexico, and passing the Straits of Florida at 
the rate of five miles an hour, forms the well-known 
current of the Gulf-stream, which sweeps along the 
whole coast of America and runs northward as far as 
the bank of Newfoundland, then bending to the east it 
flows past the Azores and Canary islands, till it joins 
the great westerly current of the tropics about latitude 
21 north. According to M. de Humboldt this great 
circuit of 3800 leagues, which the waters of the Atlantic 



SECT. XIII. CURRENTS IN THE OCEAN. 95 

are perpetually describing between the parallels of eleven 
and forty- three degrees of latitude, may be accomplished 
by any one particle in two years and ten months. In 
the center of this ^current is situated the wide field of 
floating sea-weed called the grassy sea. Besides this 
there are branches of the Gulf-stream, which convey 
the fruits, seeds, and a portion of the warmth of the 
tropical climates to our northern shores. 

The general westward motion of the South Sea, togeth- 
er with the south polar current, produce various water- 
courses in the Pacific and Indian Oceans, according as 
the one or the other prevails. The western set of the 
Pacific causes currents to pass on each side of Australia, 
while the polar stream rushes along the bay of Bengal : 
the westerly current again becomes most powerful to- 
ward Ceylon and the Maldives, whence it stretches by 
the extremity of the Indian peninsula past Madagascar, 
to the most southern point of the continent of Africa, 
where it mingles with the general motion of the seas. 
Icebergs are sometimes drifted as far as the Azores 
from the north pole, and from the south pole they have 
come even to the Cape of Good Hope. But the ice 
which encircles the south pole extends to lower latitudes 
by 10 than that which surrounds the north. In conse- 
quence of the polar current Sir Edward Parry was 
obliged to give up his attempt to reach the north pole 
in the year 1827, because the fields of ice were drifting 
to the south faster than his party could travel over them 
to the north. 

As distinct currents of air traverse the atmosphere in 
horizontal strata, so in all probability under currents in 
the ocean flow in opposite directions from those on the 
surface ; and there is every reason to believe that the 
cold waters, deep below the surface of the sea in the 
equinoctial regions, are brought by submarine currents 
from the poles, though it is not easy to prove their ex- 
istence. 



96 MOLECULAR FORCES. SBCT. XIV. 



SECTION XIV. 

Repulsive Force Interstices or Pores Elasticity Mossotti's Theory 
Gravitation brought under the same law with Molecular Attraction and 
Repulsion Gases reduced to Liquids by Pressure Intensity of the Co- 
hesive Force Effects of Gravitation Effects of Cohesion Minuteness 
of the ultimate Atoms of Matter Limited Height of the Atmosphere 
Theory of Definite Proportions and Relative Weight of Atoms Dr. Far- 
aday's Discoveries with regard to Affinity Composition of Water by a 
Plate of Platina Crystallization Cleavage Isomorphism Matter con- 
sists of Atoms of Definite Form Capillary Attraction. 

THE oscillations of the atmosphere and its action 
upon rays of light coming from the heavenly bodies, 
connect the science of astronomy with the equilibrium 
and movements of fluids, and the laws of molecular 
attraction. Hitherto that force has been under consid- 
eration which acts upon masses of matter at sensible 
distances ; but now the effects of such forces are to be 
considered as act at inappreciable distances upon the 
ultimate atoms of material bodies. 

All substances consist of an assemblage of material 
particles, which are far too small to be visible by any 
means human ingenuity has yet been able to devise, 
and which are much beyond the limits of our percep- 
tions. Since every known substance may be reduced 
in bulk by pressure, it follows that the particles of mat- 
ter are not in actual contact, but are separated by inter- 
stices, owing to the repulsive principle that maintains 
them at extremely minute distances from one another. 
It is evident that the smaller the interstitial spaces 
the greater the density. These spaces appear in 
some cases to be filled with air, as may be infer- 
red from certain semi-opaque minerals and other sub- 
stances becoming transparent when plunged into water ; 
sometimes they may possibly contain some unknown 
and highly elastic fluid, such as Sir David Brews ter has 
discovered in the minute cavities of various minerals, 
which occasionally causes these substances to explode 
with violence when under the hands of the lapidary, 
but in general they seem to our senses to be void ; yet 
as it is inconceivable that the particles of matter should 
vet upon one another without some means of commu- 



SECT. XIV. MOLECULAR FORCES. 97 

nication, tnere is eveiy reason to presume that the in- 
terstices of material substances contain a portion of that 
subtle ethereal and elastic fluid with which the regions 
of space are replete. 

Substances compressed by a sufficient force, are said 
to be more or less elastic according to the facility with 
which they regain their bulk or volume when the 
pressure is removed ; a property which depends upon 
the repulsive force of their particles, and the effort re- 
quired to compress the substance is a measure of the 
intensity of that repulsive force which varies with the 
nature of the substance. 

By the laws of gravitation the particles of matter 
attract one another when separated by sensible dis- 
tances; and as they repel each other when they are 
inappreciably near, it recently occurred to Professor 
Mossotti of Pisa, that there might be some intermedi- 
ate distance at which the particles might neither attract 
nor repel one another, but remain balanced in that 
stable equilibrium which they are found to maintain in 
every material substance solid and fluid. 

It has long been a hypothesis among philosophers 
that electricity is the agent which binds the particles of 
matter together. We are totally ignorant of the nature 
of electricity, but it is generally supposed to be an ethe- 
real fluid in the highest state of elasticity surrounding 
every particle of matter ; and as the earth and the at- 
mosphere are replete with it in a latent state, there is 
every reason to believe that it is unbounded, filling the 
regions of space. 

The celebrated Franklin was the first who explained 
the phenomena of electricity in repose, by supposing 
the molecules of bodies to be surrounded by an atmos- 
phere of the electric fluid ; and that while the electric 
atoms repel one another, they are attracted by the ma- 
terial molecules of the body. These forces of attraction 
and repulsion were afterward proved by Coulomb to 
vary inversely as the squares of the distance. The 
hypothesis of Franklin waa reduced to a mathematical 
theory by JEpinus, and the most refined analysis has 
been employed by the Baron Poisson in explanation of 
electric phenomena. Still these philosophers were un- 



98 MOSSOnTS THEORY. SECT. XIV. 

able to reconcile the attraction of the molecules of mat- 
ter inversely as the squares of the distance as proved 
by Newton, with their mutual repulsion according to 
the same law. But Professor Mossotti has recently 
shown, by a very able analysis, that there are strong 
grounds for believing that not only the molecular forces 
which unite the particles of material bodies depend on 
the electric fluid, but that even gravitation itself, which 
binds world to world and sun to sun, can no longer be 
regarded as an ultimate principle, but the residual por- 
tion of a far more powerful force generated by that en- 
ergetic agent which pervades creation. 

It is true that this connection between the molecular 
forces and gravitation depends upon a hypothesis ; but 
in the greater number of physical investigations, some 
hypothesis is requisite in the first instance to aid the 
imperfection of our senses. Yet, when the phenomena 
of nature accord with the assumption, we are justified 
in believing it to be a general law. 

As the particles of material bodies are not in actual 
contact, Professor Mossotti supposes that each is en- 
compassed by an atmosphere of the ethereal fluid; 
that the atoms of the fluid repel one another ; that the 
molecules of matter repel one another, but with less 
intensity ; and that there is a mutual attraction be- 
tween the particles of matter and the atoms of the fluid. 
Forces which we know to exist, and which he assumes 
to vary inversely as squares of: the distance. The fol- 
lowing important results have been obtained by the pro- 
fessor from the adjustment of these three forces : 

When the material molecules of a body are inappre- 
ciably near to one another, they mutually repel each 
other with a force which diminishes rapidly as the 
infinitely small distance between the material molecules 
augments, and at last vanishes. When the molecules 
are still farther apart, the force becomes attractive. At 
that particular point where the change takes place, the 
forces of repulsion and attraction balance each other, so 
that the molecules of a body are neither disposed to 
approach nor recede, but remain in equilibrio. If we 
try to press them nearer, the repulsive force resists the 
attempt ; and if we endeavor to break the body so as to 



SCT XIV. MOSSOTTPS THEORY. 99 

tear the particles asunder, the attractive force predom- 
inates and keeps them together. This is what consti- 
tutes the cohesive force, or force of aggregation, by 
which the molecules of all substances are united. The 
limits of the distance at which the negative action be- 
comes positive vary according to the temperature and 
nature of the molecules, and determine whether the 
body which they form be solid, liquid, or aeriform. 

Beyond this neutral point, the attractive force in 
creases as the distance between the molecules augments, 
till it attains a ,maximum ; when the particles are more 
apart it diminishes ; and as soon as they are separated 
by finite or sensible distances, it varies directly as their 
mass and inversely as the squares of the distance, 
which is precisely the law of universal gravitation. 

Thus on the hypothesis that the mutual repulsion 
between the electric atoms is a little more powerful 
than the mutual repulsion between the particles of mat- 
ter, the ether and: the matter attract each other with 
unequal intensities, which leave an excess .of attractive 
force constituting gravitation. As the gravitating force 
is in operation wherever there is matter, the ethereal 
electric fluid must encompass all the bodies in the uni- 
verse ; and as it is utterly incomprehensible that the 
celestial bodies should exert a reciprocal attraction 
through a void, this important investigation of Professor 
Mossotti furnishes additional presumption in favor of a 
universal ether, already all but proved by the motion of 
comets and the theory of light. 

In ae'riform fluids the particles of matter are more 
remote from each other than in liquids and solids ; but 
the pressure may be so great as to reduce an ae'riform 
fluid to a liquid, and a liquid to a solid. Dr. Faraday 
has reduced some of the gases to a liquid state by very 
great compression; but although atmospheric air is 
capable of a diminution of volume to which we do not 
know the limit, it has hitherto always retained its 
gaseous properties, and resumes its primitive volume 
the instant the pressure is removed. 

If the particles approach sufficiently near to produce 
equilibrium between the attractive and repulsive forces, 
but not near enough to admit of any influence from 



100 CONSTITUTION OF BODIES. S CT. XIV. 

their form, perfect mobility will exist among them re- 
sulting from the similarity of their attractions, and they 
will offer great resistance when compressed ; properties 
which characterize liquids in which the repulsive prin- 
ciple is greater than in the gases. When the distance 
between the particles is still less, solids are formed. 
But the nature of their structure will vary, because at 
such small distances the power of the mutual attraction 
of the particles will depend upon their form, and will 
be modified by the sides they present to one another 
during their aggregation. Besides these three condi- 
tions of matter, there are an infinite variety of others 
corresponding to the various limits at which the two 
contending forces are balanced, which may be observed 
in the fusion of metals, and other substances passing 
from hardness to toughness, viscidity, and through all 
the other stages to perfect fluidity and even to vapor. 

The effort required to break a substance is a measure 
of the intensity of the cohesive force exerted by its 
particles, which is as variable as the intensity of the 
repulsive principle. In stone, iron, steel, and all brittle 
and hard bodies, the cohesion of the particles is powerful 
but of small extent. In elastic substances, on the con- 
trary, its action is weak but more extensive. Since all 
bodies expand by heat, the cohesive force is weakened 
by an increase of temperature. 

Every particle of matter, whether it forms a con- 
stituent part of a solid, liquid, or aeriform fluid, is 
subject to the law of gravitation. The weight of the 
atmosphere, of gases and vapor, shows that they consist 
of gravitating particles. In liquids the cohesive force 
is not sufficiently powerful to resist the action of gravi- 
tation. Therefore although their component particles 
-still maintain their connection, the liquid is scattered by 
their weight, unless when it is confined in a vessel or 
has already descended to the lowest point possible, and 
assumed a level surface from the mobility of its particles 
and the influence of the gravitating force, as in the 
ocean, or a lake. Solids would also fall to pieces by 
the weight of their particles, if the force of cohesion 
were not powerful enough to resist the efforts of gravi- 
tation. 



SECT. XIV. COHESION. 101 

The phenomena arising from the force of cohesion 
are innumerable. The spherical form of rain drops ; 
the difficulty of detaching a plate of glass from the sur- 
face of water ; the force with which two plane surfaces 
adhere when pressed together; the drops that cling to 
the window-glass in'a shower of rain are all effects of 
cohesion entirely independent of atmospheric pressure, 
and are included in the same analytical formula (N. 
158) which expresses all the circumstances accurately, 
although the laws according to which the forces of 
cohesion and repulsion vary are unknown. It is more 
than probable that the spherical form of the sun and 
planets is due to the force of cohesion, as they have 
every appearance of having been at one period in a state 
of fusion. 

A very remarkable instance of cohesion has occasion- 
ally been observed hi piate-glass manufactories. After 
the large plates of glass of which the mirrors are to be 
made have received their last polish, they are carefully 
wiped and laid on their edges with their surfaces resting 
on one another. In the course of time the cohesion 
has sometimes been so powerful, that they could not be 
separated without breaking. - Instances have occurred 
where two or three have been so perfectly united, that 
they have been cut and their edges polished as if they 
had been fused together, and so great was the force 
required to make their surfaces slide that one tore off a 
portion of the surface of the other. 

The size of the ultimate particles of matter must be 
small in the extreme. Organized beings possessing life 
and all its functions, have been discovered so small that 
a million of them would occupy less space than a grain 
of sand. The malleability of gold, the perfume of 
musk, the odor of flowers, and many other instances 
might be given of the excessive minuteness of the 
atoms of matter ; yet from a variety of circumstances it 
may be inferred that matter is not infinitely divisible. 
Dr. Wollaston has shown that in all probability the 
atmospheres of the sun and planets as well as of the 
earth consist of ultimate atoms no longer divisible ; and 
if so, that our atmosphere only extends to that point 
where the terrestrial attraction is balanced by the elas- 



102 DEFINITE PROPORTIONS. SECT. XIV. 

ticity of the air. The definite proportions of chemical 
compounds afford one of the best proofs that divisibility 
of matter has a limit. The cohesive force which has 
been the subject of the preceding considerations, only 
unites particles of the same kind of matter ; whereas 
affinity, which is the cause of chemical compounds, is 
the mutual attraction between particles of different 
kinds of matter, and is merely a result of the electrical 
state of the particles, chemical affinity and electricity 
being only forms of the same powers. 

It is a permanent and universal law in all unorganized 
bodies hitherto analyzed, that the composition of sub- 
stances is definite and invariable, the same compound 
always consisting of the same elements united together 
in the same proportions. Two substances may indeed 
be mixed ; but they will not combine to form a third 
substance different from both, unless their component 
particles unite in definite proportions, that is to say, one 
part by weight of one of the substances will unite with 
one part by weight of the other, or with two parts, or 
three, or four, &c., so as to form a new substance ; but 
in any other proportions they will only be mechanically 
mixed. For example, one part by weight of hydrogen 
gas will combine with eight parts by weight of oxygen 
gas and form water ; or it will unite with sixteen parts 
by weight of oxygen, and form a substance called 
deutoxide of hydrogen ; but added to any other weight 
of oxygen, it will produce one or both of these com- 
pounds mingled with the portion of oxygen or hydrogen 
in excess. The law of definite proportion established 
by Dr. Dalton, on the principle that eveiy compound 
body consists of a combination of the atoms of its con- 
stituent parts, is of universal application, and is in fact 
one of the most important discoveries in physical science, 
furnishing information previously unhoped for with re- 
gard to the most secret and minute operations of nature, 
in disclosing the relative weights of the ultimate atoms 
of matter. Thus an atom of oxygen uniting with an 
atom of hydrogen forms the compound water ; but as 
every drop of water, however small, consists of eight 
parts by weight of oxygen and one part by weight of 
hydrogen, it follows that an atom of oxygen is eight 



Scr. XIV. CHEMICAL AFFINITY. 103 

times heavier than an atom of hydrogen. In the same 
manner sulphuretted hydrogen gas consists of sixteen 
parts by weight of sulphur and one of hydrogen ; there- 
fore, an atom of sulphur is sixteen times heavier than 
an atom of hydrogen. Also carbonic oxide is consti- 
tuted of six parts by weight of carbon, and eight of 
oxygen ; and as an atom of oxygen has eight times the 
weight of an atom of hydrogen, it follows that an atom 
of carbon is six times heavier than one of hydrogen. 
Since the same definite proportion holds in the compo- 
sition of all substances that have been examined, it may 
be concluded that there are great differences in the 
weights of the ultimate particles of matter. M. Gay 
Lussac discovered that gases unite together by their 
bulk or volumes, in such simple and definite proportions 
as one to one, one to two, one to three, &c. For 
example, one volume or measure of oxygen unites wkh 
two volumes or measures of hydrogen in the formation 
of water. 

Affinity modified by the electrical condition of the 
particles of matter, has hitherto been believed to be the 
cause of chemical combinations. However, Dr. Fara- 
day has proved by experiments, on bodies both in solu- 
tion and fusion, that chemical affinity is merely a result 
of the electrical state of the particles of matter. Now 
it must be observed that the composition of bodies as 
well as their decomposition, may be accomplished by 
means of electricity ; and Dr. Faraday has found that 
this chemical composition and decomposition, by a. given 
current of electricity, is always accomplished according 
to the laws of definite proportions ; and that the quan- 
tity of electricity requisite for the decomposition of a 
substance is exactly the quantity necessary for its com- 
position. Thus the quantity of electricity which can. 
decompose a grain weight of water is exactly equal to 
the quantity of electricity which unites the elements of 
that grain of water together, and is equivalent to the 
quantity of atmospheric electricity which is active in a 
very powerful thunder-storm. These laws are univer- 
sal, and are of that high and general order that charac- 
terize all great discoveries, and perfectly agree with 
Professor Mossotti's theory. 



104 EFFECTS OF COHESION. SECT. XIV. 

Dr. Faraday has given a singular instance of cohesive 
force inducing chemical combination, by the following 
experiment, which seems to be nearly allied to the dis- 
covery made by M. Dcebereiner, in 1823, of the spon- 
taneous combustion of spongy platina (N. 159) exposed 
to a stream of hydrogen gas mixed with common air. 
A plate of platina with extremely clean surfaces, when 
plunged into oxygen and hydrogen gas mixed in the pro- 
portions which are found in the constitution of water, 
causes the gases to combine and water to be formed, 
the platina to become red-hot, and at last an explosion 
to take place ; the only conditions necessary for this 
curious experiment being excessive purity in the gases 
and in the surface of the plate. A sufficiently pure 
metallic surface can only be obtained by immersing the 
platina in very strong hot sulphuric acid and then wash- 
ing it in distilled water, or by making it the positive 
pole of a pile in dilute sulphuric acid. It appears that 
the force of cohesion as well as the force of affinity ex- 
erted by particles of matter, extends to all the particles 
within a very minute distance. Hence the platina while 
drawing the particles of the two gases toward its sur- 
face by its great cohesive attraction, brings them so near 
to one another that they come within the sphere of their 
mutual affinity, and a chemical combination takes place. 
Dr. Faraday attributes the effect in part also to a dim- 
inution in the elasticity of the gaseous particles on their 
sides adjacent to the platina, and to their perfect mix- 
ture or association, as well as to the positive action of 
the metal in condensing them against its surface by its 
attractive force. The particles when chemically united 
run off the surface of the metal in the form of water by 
their gravitation, or pass away as aqueous vapor and make 
way for others. 

The particles of matter are so small that nothing is 
known of their form, further than the dissimilarity of 
their different sides in certain cases, which appears from 
then* reciprocal attractions during crystalization being 
more or less powerful, according to the sides they pre- 
sent to one another. Crystalization is an effect of mole- 
cular attraction regulated by certain laws, according to 
which atoms of the same kind of matter unite in regu- 



SECT. XIV. CRYSTALIZATION. 105 

lar forms a fact easily proved by dissolving a piece of 
alum in pure water. The mutual attraction of the par- 
ticles is destroyed by the water ; but if it be evaporated 
they unite and form in uniting eight-sided figures called 
octahedrons (N. 160). These, however, are not all the 
same. Some have their angles cut off, others their 
edges, and some both, while the remainder take the 
regular form. It is quite clear that the same circum- 
stances which cause the aggregation of a few particles 
would, if continued, cause the addition of more ; and 
the process would go on as long as any particles remain 
free round the primitive nucleus, which would increase 
in size, but would remain unchanged in form, the figure 
of the particles being such as to maintain the regularity 
and smoothness of the surfaces of the solid and their 
mutual inclinations. A broken crystal will by degrees 
resume its regular figure when put back again into the 
solution of alum, which shows that the internal and ex- 
ternal particles are similar and have a similar attraction 
for the particles held in solution. The original condi- 
tions of aggregation which make the molecules of the 
same substance unite in different forms must be very 
numerous, since of carbonate of lime alone there are 
many hundred varieties ; and certain it is from the mo- 
tion of polarized light through rock crystal, that a very 
different arrangement of particles is requisite to produce 
an extremely small change in external form. A variety 
of substances in crystalizing combine chemically with a 
certain portion of water which in a dry state forms an 
essential part of their crystals ; and according to the 
experiments of MM. Haidinger and Mitscherlich seems 
in some cases to give the peculiar determination to their 
constituent molecules. These gentlemen have observed 
that the same substance crystalizing at different tem- 
peratures unites with different quantities of water and 
assumes a corresponding variety of forms. Seleniate 
of zinc, for example, unites with three different portions 
of water and assumes three different forms, according 
as its temperature in the act of crystalizing is hot, luke- 
warm, or cold. Sulphate of soda, also, which crystal- 
izes at 90 of Fahrenheit without water of crystaliza- 
tion, combines with water at the ordinary temperature 



106 CRYSTALIZATION. SBCT. XIV. 

and takes a different form. Heat appears to have a 
great influence on the phenomena of crystalization, not 
only when the particles of matter are free, but even 
when firmly united, for it dissolves their union and gives 
them another determination. Professor Mitscherlich 
found that prismatic crystals of sulphate of nickel (N. 161 ) 
exposed to a summer's sun in a close vessel, had their 
internal structure so completely altered without any ex- 
terior change, that when broken open they were com- 
posed internally of octahedrons with square bases. The 
original aggregation of the internal particles had been 
dissolved, and a disposition given to arrange themselves 
in a crystaline form. 'Crystals of sulphate of magnesia 
and of sulphate of zinc, gradually heated in alcohol till it 
boils, lose their transparency by degrees, and when 
opened are found to consist of innumerable minute crys- 
tals totally different in form from the whole crystals ; 
and prismatic crystals of zinc (N. 162) are changed in a 
few seconds into octahedrons by the heat of the sun: 
other instances might be given of the influence of even 
moderate degrees of temperature on molecular attrac- 
tion in the interior of substances. It must be observed 
that these experiments give entirely new views with 
regard to the constitution of solid bodies. We are led 
from the mobility of fluids to expect great changes in 
the relative positions of their molecules, which must be 
in perpetual motion even in the stillest water or calmest 
air ; but we were not prepared to find motion to such 
an extent in the interior of solids. That their particles 
are brought nearer by cold and pressure, or removed 
farther from one another by heat, might be expected ; 
but it could not have been anticipated that their relative 
positions could be so entirely changed as to alter their 
mode of aggregation. It follows from the low temper- 
ature at which these changes are effected, that there 
is probably no portion of inorganic matter that is not in 
a state of relative motion. 

Professor Mitscherlich's discoveries with regard to 
the forms of crystalized substances, as connected with 
their chemical charcter, have thrown additional light on 
the constitution of material bodies. There is a certain 
set of crystaline forms which are not susceptible of 



8CT. XIV. ISOMORPHISM. 107 

variation, as the die or cube (N. 163), which may be 
small or large, but is invariably a solid bounded by six 
square surfaces or planes. Such also is the tetrahedron 
(N. 164) or four-sided solid contained by four equal- 
sided triangles. Several other solids belong to this class, 
which is called the Tessular system of crystalization. 
There are other crystals which, though bounded by the 
same number of sides, and having the same form, are 
yet susceptible of variation ; for instance, the eight- 
sided figure with a square base called an octahedron 
(N. 165), which is sometimes flat and low and some- 
times acute and high. It was formerly believed that 
identity of form in all crystals not belonging to the 
Tessular system indicated identity of chemical compo- 
sition. Professor Mitscherlich however has shown, 
that substances differing to a certain degree in chemical 
composition have the property of assuming the same 
crystaline form. For example, the neutral phosphate 
of soda and the arseniate of soda crystalize in the very 
same form, contain the same quantities of acid, alkali, 
and water of crystalization ; yet they differ so far, that 
one contains arsenic and the other an equivalent quan- 
tity of phosphorus. Substances having such properties 
are said to be isomorphous, that is, equal in form. Of 
these there are many groups, each group having the 
same form, and similarity though not identity of chemi- 
cal composition. For instance, one of the isomorphous 
groups is that consisting of certain chemical substances 
called the protoxides of iron, copper, zinc, nickel, and 
manganese, all of which are identical in form and contain 
the same quantity of oxygen, but differ in the respective 
metals they contain, which are however nearly in the 
same proportion in each. All these circumstances tend 
to prove that substances having the same crystaline form 
must consist of ultimate atoms, having the same figure 
and arranged in the very same order ; so that the form 
of crystals is dependent on their atomic constitution. 

All crystalized bodies have joints called cleavages, at 
which they split more easily than in other directions ; 
on this property the whole art of cutting diamonds de- 
pends. Each substance splits in a manner and informs 
peculiar to itself. For example, all the hundreds of 



108 CLEAVAGE. SECT. XIV. 

forms of carbonate of lime split into six-sided figures, 
called rhombohedrons (N. 166), whose alternate angles 
measure 105*55 and 75-05, however far the division 
may be carried ; therefore the ultimate particle of car- 
bonate of lime is presumed to have that form. However 
this may be, it is certain that all the various crystals of 
that mineral may be formed by building up six-sided 
solids of the form described, in the same manner as chil- 
dren build houses with miniature bricks. It may be 
imagined that a wide difference may exist between the 
particles of an unformed mass,, and a crystal of the same 
substance between the common shapeless limestone 
and the pure and limpid crystal of Iceland spar, yet 
chemical analysis detects none ; their ultimate atoms 
are identical, and crystalization shows that the difference 
arises only from the mode of aggregation. Besides, all 
substances either crystalize naturally, or may be made to 
do so by art. Liquids crystalize in freezing, vapors by 
sublimation (N. 167) ; and hard bodies, when fused, crys- 
talize in cooling. Hence it may be inferred that all sub- 
stances are composed of atoms, on whose magnitude, 
density, and form their nature and qualities depend ; 
and as these qualities are unchangeable, the ultimate 
particles of matter must be incapable of wear the same 
now as when created. 

The oscillations of the atmosphere and the changes 
in its temperature, are measured by variations in the 
heights of the barometer and thermometer. But the 
actual length pf the liquid columns depends not only upon 
the force of gravitation, but upon the cohesive force, or 
reciprocal attraction between the molecules of the liquid 
and those of the tube containing it. This peculiar action 
of the cohesive force is called capillary attraction or ca- 
pillarity. If a glass tube of extremely fine bore, such as 
a small thermometer tube, be plunged into a cup of wa- 
ter or spirit of wine, the liquid will immediately rise in 
the tube above the level of that in the cup ; and the sur- 
face of the little column thus suspended will be a hollow 
hemisphere, whose diameter is the interior diameter of 
the tube. If the same tube be plunged into a cupful of 
mercury the liquid will also rise in the tube, but it will 
never attain the level of that in the cup, and its surfnce 



SECT. XIV. CAPILLARY ATTRACTION. 109 

will be a hemisphere whose diameter is also the diame- 
ter of the tube (N. 168). The elevation or depression 
of the same liquid in different tubes of the same matter, 
is in the inverse ratio of their internal diameters (N. 169), 
and altogether independent of their thickness ; whence 
it follows that the molecular action is insensible at sen- 
sible distances, and that it is only the thinnest possi- 
ble film of the interior surface of the tubes that exerts a 
sensible action on the liquid. So much indeed is this 
the case, that when tubes of the same bore are com- 
pletely wetted with water throughout their whole ex- 
tent, mercury will rise to the same height in all of them, 
whatever be their thickness or density, because the mi- 
nute coating of moisture is sufficient to remove the in- 
ternal column of mercury beyond the sphere of attraction 
of the tube, and to supply the place of a tube by its 
own capillary attraction. The forces which produce the 
capillary phenomena are the reciprocal attraction of the 
tube and the liquid, and of the liquid particles on one 
another ; and in order that the capillary column may be 
in equilibrio, the weight of that part of it which rises 
above or sinks below the level of the liquid in the cup 
must balance these forces. 

The estimation of the action of the liquid is a difficult 
part of this problem. La Place, Dr. Young, and other 
mathematicians, have considered the liquid within the 
tube to be of uniform density ; but M. Poisson, in one 
of those masterly productions in which he elucidates the 
most abstruse subjects, has proved that the phenomena 
of capillary attraction depend upon a rapid decrease in 
the density of the liquid column throughout an extremely 
small space at its surface. Every indefinitely thin layer 
of a liquid is compressed by the liquid above it, and sup- 
ported by that below. Its degree of condensation de- 
pends upon the magnitude of the compression force ; 
and as this force decreases rapidly toward the surface 
where it vanishes, the density of the liquid decreases 
also. M. Poisson has shown that when this force is 
omitted, the capillary surface becomes plane, and that 
the liquid in the tube will neither rise above nor sink 
below the level of that in the cup. In estimating the 
forces, it is also necessary to include the variation in the 
K. 



110 CAPILLARY ATTRACTION. SHCT. XIV. 

density of the capillary surface round the edges from the 
attraction of the tube. 

The direction of the resulting force determines the 
curvature of the surface of the capillary column. In 
order that a liquid may be in equilibrio, the force re- 
sulting from all the forces acting upon it must be per- 
pendicular to the surface. Now it appears that as glass 
is more dense than water or alcohol, the resulting force 
will be inclined toward the interior side of the tube ; 
therefore the surface of the liquid must be more ele- 
vated at the sides of the tube than in the center in order 
to be perpendicular to it, so that it will be concave as in 
the thermometer. But, as glass is less dense than mer- 
cury, the resulting force will be inclined from the interior 
side of the tube (N. 170), so that the surface of the ca- 
pillary column must be more depressed at the sides of 
the tube than in the center, in order to be perpendicular 
to the resulting force, and is consequently convex, as 
may be perceived in the mercury of the barometer when 
rising. The absorption of moisture by sponges, sugar, 
salt, &c., are familiar examples of capillary attraction. 
Indeed the pores of sugar are so minute, that there 
seems to be no limit to the ascent of the liquid. Wine 
is drawn up in a curve on the interior surface of a glass ; 
tea rises above its level on the side of a cup ; but if the 
glass or cup be too full, the edges attract the liquid 
downward, and give it a rounded form. A column of 
liquid will rise above or sink below its level between two 
plane parallel surfaces when near to one another, ac- 
cording to the relative densities of the plates and the 
liquid (N. 171) ; and the phenomena will be exactly the 
same as in a cylindrical tube whose diameter is double 
the distance of the plates from each other. If the two 
surfaces be very near to one another, and touch each 
other at one of their upright edges, the liquid will rise 
highest at the edges that are in contact, and will grad- 
ually diminish in height as the surfaces become more 
separated. The whole outline of the liquid column will 
have the form of a hyperbola. Indeed so universal is 
the action of capillarity, that solids and liquids cannot 
touch one another without producing a change in the 
form of the surface of the liquid. 



SBCT. XV. CAPILLARY ATTRACTION. Ill 

The attractions and repulsions arising from capillarity 
present many curious phenomena. If two plates of 
glass or metal, both of which are either dry or wet, be 
partly immersed in a liquid parallel to one another, the 
liquid will be raised or depressed close to their surfaces, 
but will maintain its level through the rest of the space 
that separates them. At such a distance they neither 
attract nor repel one another ; but the instant they are 
brought so near as to make the level part of the liquid 
disappear, and the two curved parts of it meet, the two 
plates will rush toward each other and remain pressed 
together (N. 172). If one of the surfaces be wet and 
the other dry, they will repel one another when so near 
as to have a curved surface of liquid between them ; but 
if forced to approach a little nearer the repulsion will be 
overcome, and they will attract each other as if they 
were both wet or both dry. Two balls of pith or wood 
floating in water, or two balls of tin floating in mercury, 
attract one another as soon as they are so near that the 
surface of the liquid is curved between them. Two 
ships in the ocean may be brought into collision by this 
principle. But two balls, one of which is wet and the 
other dry, repel one another as soon as the liquid which 
separates them is curved at its surface. A bit of tea 
leaf is attracted by the edge of the cup if wet and re- 
pelled when dry, provided it be not too far from the 
edge and the cup moderately full ; if too full, the con- 
trary takes place. It is probable that the rise of the 
sap in vegetables is in some degree owing to capillarity. 



SECTION XV. 

Analysis of the Atmosphere Its Pressure Law of Decrease in Density- 
Law of Decrease in Temperature Measurement of Heights by the 
Barometer Extent of the Atmosphere Barometrical Variations Oscil- 
lations Trade Winds Monsoons Rotation of Winds Laws of Hur- 
ricanes Water-Spouts. 

THE atmosphere is not homogeneous. It appears 
from analysis that of 100 parts 79 are azotic gas, and 21 
oxygen, the great source of combustion and animal heat. 
Besides these there are three or four parts of carh 



112 DENSITY OF THE ATMOSPHERE. SECT. XV. 

acid gas in 1000 parts of atmospheric air. These pro- 
portions are found to be the same at all heights hitherto 
attained by man. The air is an elastic fluid resisting 
pressure in every direction, and is subject to the law of 
gravitation. As the space in the top of the tube of a 
barometer is a vacuum, the column of mercury sus- 
pended by the pressure of the atmosphere on the sur- 
face of the cistern is a measure of its weight. Conse- 
quently every variation in the density occasions a cor- 
responding rise or fall in the barometrical column. The 
pressure of the atmosphere is about fifteen pounds on 
every square inch; so that the surface of the whole 
globe sustains a weight of 11,449,000,000 hundreds of 
millions of pounds. Shell-fish which have the power of 
producing a vacuum, adhere to the rocks by a pressure 
of fifteen pounds upon every square inch of contact. 

Since the atmosphere is both elastic and heavy, its 
density necessarily diminishes in ascending above the 
surface of the earth ; for each stratum of air is com- 
pressed only by the weight above it. Therefore the 
upper strata are less dense, because they are less com- 
pressed than those below them. Whence it is easy to 
show, supposing the temperature to be constant, that if 
the heights above the earth be taken in increasing 
arithmetical progression that is, if they increase by 
equal quantities, as by a foot or a mile, the densities of 
the strata of air, or the heights of the barometer which 
are proportionate to them, will decrease in geometrical 
progression. For example, at the level of the sea, if the 
mean height of the barometer be 29-922 inches, at the 
height of 18,000 feet it will be 14-961 inches, or one 
half as great; at the height of 36,000 feet, it will be one 
fourth as great; at 54,000 feet, it will be one eighth, 
and so on, which affords a method of measuring the 
heights of mountains with considerable accuracy, and 
would be very simple, if the decrease in the density of 
the air were exactly according to the preceding law. 
But it is modified by several circumstances, and chiefly 
by changes of temperature, because heat dilates the 
air and cold contracts it, varying ] F of the whole bulk 
when at 32, for every degree of Fahrenheit's ther- 
mometer. Experience shows that the heat of the air 



8cr. XV. BAROMETRICAL MEASUREMENTS. 113 

decreases as the height above the surface of the earth 
increases. And it appears from recent investigations 
that the mean temperature of space is 58 below the 
zero point of Fahrenheit, which would probably be the 
temperature of the surface of the earth also were it 
not for the non-conducting power of the air, whence it 
is enabled to retain the heat of the sun's rays, which 
the earth imbibes and radiates in all directions. The 
decrease in heat is very irregular ; each authority gives 
a different estimate : probably because the decrease 
varies with the latitude as well as the height, and some- 
thing is due also to local circumstances. But from the 
mean of five different statements, it seems to be about 
one degree for every 334 feet, which is the cause of the 
severe cold and eternal snows on the summits of the 
Alpine chains. Of the various methods of computing 
heights from barometrical measurements, that of Mr. 
Ivory has the advantage of combining accuracy with the 
greatest simplicity. Indeed the accuracy with which 
the heights of mountains can be obtained by this method 
is very remarkable. Captain Smyth, R.N., and Sir 
John Herschel measured the height of Etna by the 
barometer without any communication ^and hi different 
years; Captain Smyth made it 10,874 feet, and Sir John 
Herschel 10,873 ; the difference being only one foot. In 
consequence of the diminished pressure of the atmos- 
phere, water boils at a lower temperature on the moun- 
tain tops than in the valleys, which induced Fahrenheit 
to propose this mode of observation as a method of as- 
certaining then* heights. It is very simple, as Professor 
Forbes has ascertained that the temperature of the boil- 
ing point varies in an arithmetical proportion with the 
height, or 549-5 feet for every degree of Fahrenheit, so 
that the calculation of height becomes one of arithmetic 
only without the use of any table. 

The atmosphere when in equilibrio is an ellipsoid 
flattened at the poles from its rotation with the earth. 
In that state its strata are of uniform density at equal 
heights above the level of the sea, and it is sensible of 
finite extent when it consists of particles infinitely divisi- 
ble or not. On the latter hypothesis it must really be 
finite, and even if its particles be infinitely divisible it is 
8 IL2 



114 EXTENT OF THE ATMOSPHERE. SECT. XV. 

known by experience to be of extreme tenuity at very 
small heights. The barometer rises in proportion to 
the super-incumbent pressure. At the level of the sea 
in the latitude of 45 and at the temperature of melting 
ice, the mean height of the barometer being 29-922 
inches, the density of the air is to the density of a simi- 
lar volume of mercury as 1 to 10477-9. Consequently 
the height of the atmosphere supposed to be of uniform 
density would be about 4-95 miles. But as the density 
decreases upward in geometrical progression it is consid- 
erably higher, probably about fifty miles ; at that height 
it must be of extreme tenuity, for the decrease in density 
is so rapid that three fourths of all the air contained in 
the atmosphere is within four miles of the earth ; and, 
as its superficial extent is 200 millions of square miles, 
its relative thickness is less than that of a sheet of paper 
when compared with its breadth. The air even on 
mountain tops is sufficiently rare to diminish the intensity 
of sound, to affect respiration, and to occasion a loss of 
muscular strength. The blood burst from the lips and 
ears of M. de Humboldt^as he ascended the Andes; 
and he experienced the same difficulty in kindling and 
maintaining a fire at great heights which Marco Polo 
the Venetian felt on the mountains of Central Asia. M. 
Gay-Lussac and M. Biot ascended in a balloon to the 
height of 4-36 miles, which is the greatest elevation that 
man has attained, and they suffered greatly from the 
rarity of the air. It is true that at the height of thirty- 
seven miles, the atmosphere is still dense enough to 
reflect the rays of the sun when 18 below the horizon ; 
but the tails of comets show that extremely attenuated 
matter is capable of reflecting light. And although, at 
the height of fifty miles, the bursting of the meteor of 
1783 was heard on earth like the report of a cannon, it 
only proves the immensity of the explosion of a mass 
half a mile in diameter, which could produce a sound 
capable of penetrating air three thousand times more 
rare than that we breathe. But even these heights are 
extremely small when compared with the radius of the 
earth. 

The mean pressure of the atmosphere is not the same 
all over the globe. It is less at the equator than at the 



SKCT. XV. ACTION OP THE SUN AND MOON. 115 

tropics or in the higher latitudes, in consequence of the 
ascent of the heated air from the surface of the earth ; 
it is less also on the shores of the Baltic sea than it is 
in France, probably from some permanent eddy in the 
air arising from the conformation of the surrounding 
land ; and to similar local causes those barometric depres- 
sions may be attributed which have been observed by 
M. Erman, near the Sea of Ochotzk in Eastern Siberia, 
and by Captain Foster near Cape Horn. 

There are various periodic oscillations in the atmos- 
phere which, rising and falling like waves in the sea, 
occasion corresponding changes in the height of the 
barometer, but they differ as much from the trade winds, 
monsoons, and other currents, as the tides of the sea do 
from the Gulf-stream and other oceanic rivers. The 
sun and moon disturb the equilibrium of the atmosphere 
by their attraction, and produce annual undulations which 
have their maximum altitudes at the equinoxes and their 
minima at the solstices. There are also lunar tides 
which ebb and flow twice in the course of a lunation. 
The diurnal tides, which accomplish their rise and fall 
in six hours, are greatly modified by the heat of the 
sun. Between the tropics the barometer attains its 
maximum height about nine hi the morning, then sinks 
till three or four in the afternoon; it again rises and 
attains a second maximum about nine in the evening, 
and then it begins to fall and reaches a second minimum 
at three in the morning, again to pursue the same course. 
According to M. Bouvard, the amount of the oscillations 
at the equator is proportional to the temperature, and 
in other parallels it varies as the temperature and the 
square o'f the cosine of the latitude conjointly, conse- 
quently it decreases from the equator to the poles, but 
it is somewhat greater in the day than in the night. 

Besides these small undulations, there are vast waves 
perpetually moving over the continents and oceans in 
separate and independent systems, being confined to 
local yet very extensive districts, probably occasioned by 
long-continued rains or dry weather over large tracts of 
country. By numerous barometrical observations made 
simultaneously in both hemispheres, the courses of sev- 
eral have been traced, some of which occupy twenty -four 



116 THE TRADE;- WINDS. SBCT. xv. 

and others thirty-six hours to accomplish their rise and 
fall. One especially of these vast barometric waves, many 
hundreds of miles in breadth, has been traced over the 
greater part of Europe, and not its breadth only, but also 
the direction of its front and its velocity have been clearly 
ascertained. Although like ah 1 other waves these are 
but moving forms, yet winds arise dependent on them 
like tide streams in the ocean. Mr. Birt has deter- 
mined the periods of other waves of still greater extent 
and duration, two of which require seventeen days to 
rise and fall, and another took thirteen days to complete 
its undulation. Since each oscillation has its perfect 
effect independently of the others, each one is marked 
by a change in the barometer, and this is beautifully 
illustrated by curves constructed from a series of obser- 
vations. The general form of the curve shows the 
course of the principal wave, while small undulations in 
its outline mark the maxima and minima of the minor 
oscillations. 

The trade-winds, which are the principal currents in 
the atmosphere, are only a particular case of those very 
general laws which regulate the motion of the winds 
depending on the rarefaction of the air combined with 
the rotation of the earth on its axis. 

The heat of the sun occasions these ae'rial currents 
by rarefying the air at the equator, which causes the 
cooler and more dense part of the atmosphere to rush 
along the surface of the earth from the poles toward the 
equator, while that which is heated is carried along the 
higher strata to the poles, forming two counter-currents 
in the direction of the meridian. But the rotatory ve- 
locity of the air corresponding to its geographical posi- 
tion decreases toward the poles. In approaching the 
equator it must therefore revolve more slowly than the 
corresponding parts of the earth, and the bodies on the 
surface of the earth must strike against it with the ex- 
cess of their velocity, and by its reaction they will meet 
with a resistance contrary to their motion of rotation. 
So that the wind will appear to a person supposing him- 
self to be at rest, to blow in a direction nearly though 
not altogether contrary to the earth's rotation ; because 
these currents will still retain a part of their northerly 



SicT. XV. THE TRADE-WINDS. 117 

and southerly impetus, which, combining with their de- 
ficiency of rotatory velocity, will make them appear to 
blow from the north-east on one side of the equator and 
from the south-east on the other, which is the general 
direction of the trade-winds. But they are modified 
both hi intensity and direction by the seasons, by the 
neighborhood of continents, and by the nature of the 
soil, so that the phenomena are not the same in both 
hemispheres. These winds, however, are not felt at all 
under the line, because the easterly tendency of the 
two great polar currents is gradually diminished as they 
approach the equator by the friction of the earth, which 
slowly imparts a portion of its rotatory velocity to them 
as they pass along, and when they meet in the equator 
they destroy one another's impetus. The equator does 
not exactly coincide with the line which separates the 
trad^-winds north and south of it. That line of separa- 
tion depends upon the total difference of heat in the two 
hemispheres, arising from the distribution of land and 
water, and other causes. 

The polar currents from defect of rotatory velocity 
tend, by their friction near the equator, to r diminish the 
velocity of the earth's rotation ; while, on the contrary, 
the equatorial or upper currents carry their excess of 
rotatory velocity north and south. And as they occa- 
sionally come to the surface in their passage to the poles, 
they act on the earth by their friction as a strong south- 
west wind in the northern hemisphere, and as a north- 
west wind in the southern. In this manner the equili- 
brium of rotation is maintained. Sir John Herschel 
ascribes to this cause the western and south-western 
gales so prevalent in our latitudes, and also the west 
winds which are so constant in the North Atlantic. 

There are many proofs of the existence of the coun- 
ter-currents above the trade-winds. On the Peak of 
Teneriffe the prevailing winds are from the west. The 
ashes of the volcano of St. Vincent's, in the year 1812, 
were carried to windward as far as Barbadoes by the 
upper current. The captain of a Bristol ship declared 
that on that occasion dust from St. Vincent's fell to the 
depth of five inches on the deck at the distance of 500 
miles to the eastward. Light clouds have frequently 



118 THE MONSOONS. SKCT. XV. 

been seen moving rapidly from west to east, at a very 
great height above the trade-winds, which were sweep- 
ing along the surface of the ocean in a contrary direc- 
tion. Rains, clouds, and nearly all the other atmos- 
pheric phenomena occur below the height of 18,000 
feet, and generally much nearer to the surface of the 
earth. They are owing to currents of air running upon 
each other in horizontal strata, and differing in their 
electric state, in temperature and moisture, as well as 
in velocity and direction. 

The monsoons are steady currents six months in du- 
ration, owing to diminished atmospheric pressure at each 
tropic alternately from the heat of the sun, thereby pro- 
ducing a regular alternation of north and south winds, 
which combining their motion with that of the earth on 
its axis become a north-east wind in the northern hem- 
isphere and a south-west in the southern ; the former 
blows from April to October and the latter from October 
to April. The change from one to the other is at- 
tended by violent rains, with storms of thunder and 
lightning. From some peculiar conformation of the 
land and water, these winds are confined to the Arabian 
Gulf, the Indian Ocean, and the China Sea. 

When north and south winds blow alternately, the 
wind at any place will veer in one uniform direction 
through every point of the compass, provided the one 
begins before the other has ceased. In the northern 
hemisphere a north wind sets out with a smaller degree 
of rotatory motion than the places have at which it suc- 
cessively arrives, consequently it passes through all the 
points of the compass from N. to N. E. and E. A cur- 
rent from the south, on the contrary, sets out with a 
greater rotatoiy velocity than the places have at which 
it successively arrives, so by the rotation of the earth it 
is deflected from S. to S. W. and W. Now if the vane 
at any place should have veered from the N. through 
N. E. to E. r and a south wind should spring up, it would 
combine its motion with the former and cause the vane 
to turn successively from the E. to S. E. and S. But 
by the earth's rotation this south wind will veer to the 
S. W. and W., and if a north wind should now arise, it 
would combine its motion with that of the west and 



SBCT. XV. HURRICANES. 119 

cause it to veer to the N. W. and N. Thus two alter- 
nations of north and south wind will cause the vane at 
any place to go completely round the compass, from N. 
to E., S., W., and N. again. At the Royal Observatory 
at Greenwich, the wind accomplishes five circuits in that 
direction in the course of a year. When circumstances 
combine to produce alternate north and south winds in 
the southern hemisphere, the gyration is in the contrary 
direction. Although the general tendency of the wind 
may be rotatoiy, and is so in many instances, at least 
for part of the year, yet it is so often counteracted by 
local circumstances, that the winds are in general very 
irregular ; every disturbance in atmospheric equilibrium 
from heat or any other cause producing a corresponding 
wind. The most prevalent winds in Europe are the 
N. E. and S. W. ; the former arises from the north 
polar current, and the latter from causes already men- 
tioned. The law of the wind's rotation was noticed by 
Dr. Dalton, but has been developed by Professor Dove, 
of Berlin. 

Hurricanes are those storms of wind in which the 
portion of the atmosphere that forms them revolves in a 
horizontal circuit round a vertical or somewhat inclined 
axis of rotation, while the axis itself, and consequently 
the whole storm, is carried forward along the surface of 
the globe, so that the direction in which the storm is 
advancing is quite different from the direction in which 
the rotatory current may be blowing at any point. In 
the West Indies, where hurricanes are frequent and 
destructive, they generally originate in the tropical 
regions near the inner boundary of the trade-winds, and 
are probably owing to a portion of the superior current 
of wind penetrating through the lower. By far the 
greater number of Atlantic hurricanes have begun 
eastward of the lesser Antilles or Caribbean Islands. 

In every case the axis of the storm moves in an 
elliptical or parabolic curve, having its vertex hi or near 
the tropic of Cancer, which marks the external limit of 
the trade-winds north of the equator. As the motion 
before it reaches the tropic is in a straight line from S. 
E. to N. W., and after it has passed it from S. W. to 
N. E., the bend of the curve is turned toward Florida 



120 HURRICANES. SECT. XV. 

and the Carolinas. In the southern hemisphere the 
body of the storms moves in exactly the opposite direc- 
tion. The hurricanes which originate south of the 
equator, and whose initial path is from N. E. to S. W., 
bend round at the tropic of Capricorn, and then bend 
from N. W. to S. E. 

The extent and velocity of these storms are great ; 
for instance, the hurricane that took place on the 12th 
of August, 1830, was traced from the eastward of the 
Caribbee Islands to the bank of Newfoundland, a distance 
of more than 3000 miles, which it passed over in six 
days. Although the hurricane of the 1st of September, 
1821, was not so extensive, its velocity was greater, as 
it moved at the rate of 30 miles an hour : small storms 
are generally more rapid than those of greater dimen- 
sions. 

The action of these storms seems to be at first con- 
fined to the stratum of air nearest the earth, and then 
they seldom appear to be more than a mile high, 
though sometimes they are raised higher ; or even 
divided by a mountain into two separate storms, each of 
which continues its new path and gyrations with in- 
creased violence. This occurred in the gale of the 25th 
of December, 1821, in the Mediterranean, when the 
Spanish mountains and the Maritime Alps became new 
centers of motion. 

By the friction of the earth the axis of the storm 
bends a little forward, so that the whirling motion begins 
in the higher regions of the atmosphere before it is felt 
on the earth. This causes a continual intermixture ot 
the lower and warmer strata of air with those that are 
higher and colder, producing torrents of rain and violent 
electric explosions. 

The rotation is different in direction in different hemi- 
spheres, though always alike in the same. In the 
northern hemisphere the gyration is contrary to the 
movement of the hands of a watch, that is to say, the 
wind revolves from east round through the north to the 
west, south and east again ; while in the southern hemi- 
sphere, the rotation about the axis of the storm is in the 
contrary direction. 

The breadth of the whirlwind is greatly augmented 



8cr. XV. HURRICANES. 121 

when the path of the storm changes on crossing the 
tropic. The vortex of a storm has covered an extent of 
the surface of the globe 500 miles in diameter. 

The revolving motion accounts for the sudden and 
violent changes observed during hurricanes. In conse- 
quence of the rotation of the air, the wind blows in op- 
posite directions on each side of the axis of the storm, 
and the violence of the blast increases from the circum- 
ference toward the center of gyration, but hi the center 
itself the ah- is in repose : hence, when the body of the 
storm passes over a place, the wind begins to blow mod- 
erately, and increases to a hurricane as the center of 
the whirlwind approaches ; then, in a moment, a dead 
and awful calm succeeds, suddenly followed by a re- 
newal of the storm in all its violence, but now blowing 
in a direction diametrically opposite to its former course. 
This happened at the Island of St. Thomas, on the 2d 
of August, 1837, where the hurricane increased in vio- 
lence till half-past seven in the morning, when perfect 
stillness took place for forty minutes, after which the 
storm recommenced in a contrary direction. 

The sudden fell of the mercury in the barometer in 
the regions habitually visited by hurricanes is a certain 
indication of a coming tempest. In consequence of the 
centrifugal force of these rotatory storms the air be- 
comes rarefied, and as the atmosphere is disturbed to 
some distance beyond the actual circle of gyration or 
limits of the storm, the barometer often sinks some 
hours before its arrival, from the original cause of the 
rotatory disturbance. It continues sinking under the 
first half of the hurricane, and again rises during the 
passage of the latter half, though it does not attain its 
greatest height till the storm is over. The diminution 
of atmospheric pressure i greater and extends over a 
wider area in the temperate zones than in the torrid, 
on account of the sudden expansion of the circle of rota- 
tion when the gale crosses the tropic. 

As the fall of the barometer gives warning of the ap- 
proach of a hurricane, so the laws of the storm's mo- 
tion afford to the seaman the knowledge to guide him in 
avoiding it. In the northern temperate zone, if the gale 
begins from the S. E. and veers by S. to W., the ship 
L 



136 THEORY OF SOUND. SECT. XVI 

should steer to the S. E. ; but if the gale begins from 
the N. E., and changes through N. to N. W., the ves- 
sel should go to the N. W. In the northern part of the 
torrid zone, if the storm begin from the N. E. and veer 
through E. to S. E., the ship should steer to the N. E. ; 
but if it begin from the N. W. and veer by W. to S. W., 
the ship should steer to the S. W., because she is in the 
south-western side of the storm. Since the laws of 
storms are reversed in the southern hemisphere, the 
rules for steering vessels are necessarily reversed also. 
A heavy swell is peculiarly characteristic of these 
storms. In the open sea the swell often extends many 
leagues beyond the range of the gale which produced it. 
Waterspouts are occasioned by small whirlwinds, 
which always have their origin at a great distance from 
that part of the sea from which the spout begins to rise, 
where it is generally calm. The whirl of the air be- 
gins in the clouds, and extending downward to the sea, 
causes the water to ascend in a spiral by the impulse of 
the centrifugal force. When waterspouts have a pro- 
gressive motion, the vortex of air in the cloud above 
must move with the same velocity, otherwise the spouts 
break, which frequently happens. 



SECTION XVI. 

Sound Propagation of Sound illustrated by a Field of Standing Corn 
Nature of Waves Propagation of Sound through the Atmosphere 
Intensity Noises A Musical Sound Quality Pitch Extent of 
Human Hearing Velocity of Sound in Air, Water, and Solids Causes 
of the Obstruction of Sound Law of its Intensity Reflection of Sound 
Echoes Thunder Refraction of Sound Interference of Sounds. 

ONE of the most important uses of the atmosphere is 
the conveyance of sound. Without the air deathlike 
silence would prevail through nature, for in common 
with all substances it has a tendency to impart vibrations 
to bodies in contact with it. Therefore undulations re- 
ceived by the air, whether it be from a sudden impulse 
such as an explosion or the vibrations of a musical chord, 
are propagated in every direction, and produce the sen- 
sation of sound upon the auditory nerves. A bell rung 
under the exhausted receiver of an air-pump is inaudi- 



SCT. XVI. UNDULATIONS OF OOBN. 123 

ble, which shows that the atmosphere is really the me- 
dium of sound. In the small undulations of deep water 
in a calm, the vibrations of the liquid particles are made 
m the vertical plane, that is up and down, or at right 
angles to the direction of the transmission of the waves. 
But the vibrations of the particles of ah* which produce 
sound differ from these, being performed in the same 
direction in which the waves of sound travel. The 
propagation of sound has been illustrated by a field of 
corn agitated by the wind. However irregular the 
motion of the corn may seem on a superficial view, it 
will be found, if the velocity of the wind be constant, 
that the waves are all* precisely similar and equal, and 
that all are separated by equal intervals and move in 
equal times. 

A sudden blast depresses each ear equally and suc- 
cessively in the direction of the wind, but in conse- 
quence of the elasticity of the stalks and the force of 
the impulse, each ear not only rises again as soon as 
the pressure is removed, but bends back nearly as 
much in the contrary direction, and then continues to 
oscillate backward and forward in equal times, like a 
pendulum to a less and less extent, till the resistance of 
the air puts a stop to the motion. These vibrations are 
the same for every individual ear of corn. Yet as their 
oscillations do not all commence at the same time, but 
successively, the ears will have a variety of positions at 
any one instant. Some of the advancing ears will meet 
others in their returning vibrations, and as the times of 
oscillation are equal for all, they will be crowded to- 
gether at regular intervals. Between these there will 
occur equal spaces, where the ears will be few, in con- 
sequence of being bent in opposite directions ; and at 
other equal intervals they will be in their natural upright 
positions. So that over the whole field there will be a 
regular series of condensations and rarefactions among 
the ears of corn, separated by equal intervals where 
they will be in their natural state of density. In con- 
sequence of these changes the field will be marked by 
an alternation of bright and dark bands. Thus the 
successive waves which fly over the corn with the 
speed of the wind, are totally distinct from, and entirely 



134 UNDULATIONS OF THE AIR. SECT. XVI. 

independent of the extent of the oscillations of each in- 
dividual ear, though both take place in the same direc- 
tion. The length of a wave is equal to the space be- 
tween two ears precisely in the same state of motion, 
or which are moving similarly, and the time of the vi- 
bration of each ear is equal to that which elapses be- 
tween the arrival of two successive waves at the same 
point. The only difference between the undulations of 
a corn-field and those of the air which produce sound 
is, that each ear of corn is set in motion by an external 
cause and is uninfluenced by the motion of the rest ; 
whereas in air, which is a compressible and elastic fluid, 
when one particle begins to oscillate, it communicates 
its vibrations to the surrounding particles, which trans- 
mit them to those adjacent, and so on continually. 
Hence from the successive vibrations of the particles of 
air the same regular condensations and rarefactions take 
place as in the field of corn, producing waves through- 
out the whole mass of air, though each molecule, like 
each individual ear of corn, never moves far from its 
state of rest. The small waves of a liquid and the un- 
dulations of the air like waves in the corn, are evidently 
not real masses moving in the direction in which they 
are advancing, but merely outlines, motions, or forms 
passing along, and comprehending all the particles of an 
undulating fluid which are at once in a vibratory state. 
It is thus that an impulse given to any one point of the 
atmosphere is successively propagated in all directions, 
in a wave diverging as from the center of a sphere to 
greater and greater distances, but with decreasing in- 
tensity, in consequence of the increasing number of par- 
ticles of inert matter which the force has to move ; like 
the waves formed in still water by a falling stone, which 
are propagated circularly all around the center of' dis- 
turbance (N. 156). 

The intensity of sound depends upon the violence 
and extent of the initial vibrations of air ; but whatever 
they may be, each undulation when once formed can 
only be transmitted straight forward, and never returns 
back again unless when reflected by an opposing ob- 
stacle. The vibrations of the aSrial molecules are al- 
ways extremely small, whereas the waves of sound 



. XVI. EXTENT OP HEARING. 125 

vary from a few inches to several feet. The various 
musical instruments, the human voice and that of ani- 
mals, the singing of birds, the hum of insects, the roar 
of the cataract, the whistling of the wind, and the other 
nameless peculiarities of sound, show at once an infinite 
variety in the modes of ae'rial vibration, and the aston- 
ishing acuteness and delicacy of the ear, thus capable of 
appreciating the minutest differences in- the laws of 
molecular oscillation. 

All mere noises are occasioned by irregular impulses 
communicated to the ear, and if they be short, sudden, 
and repeated beyond a certain degree of quickness, the 
ear loses the intervals of silence and the sound appears 
continuous. Still such sounds will be mere noise: in 
order to produce a musical sound, the impulses, and 
consequently the undulations of the air must be all ex- 
nctly similar in duration and intensity, and must recur 
after exactly equal intervals of time. If a blow be given 
to the nearest of a series of broad, flat, and equidistant 
palisades set edgewise in a line direct from the ear, 
each palisade will repeat or echo the sound ; and these 
echoes returning to the ear at successive equal intervals 
of time will produce a musical note. The quality of a 
musical note depends upon the abruptness, and its in- 
tensity upon the violence and extent of the original im- 
pulse. In the theory of harmony the only property of 
sound taken into consideration is the pitch, which varies 
with the rapidity of the vibrations. The grave or low 
tones are produced by very slow vibrations, which in- 
crease in frequency as the note becomes more acute. 
Very deep tones are not heard by all alike, and Dr. Wol- 
laston, who made a variety of experiments on the sense 
of hearing, found that many people though not at all 
deaf are quite insensible to the cry of the bat or the 
cricket, while to others it is painfully shrill. From his 
experiments he concluded that human hearing is limited 
to about nine octaves, extending from the lowest note of 
the organ to the highest known cry of insects ; and he 
observes with his usual originality that, " as there is 
nothing in the nature of the atmosphere to prevent the 
existence of vibrations incomparably more frequent than 
any of which we are conscious, we may imagine that 
1,2 



126 EXPERIMENTS OP M. SAVART. SKCT. XVI. 

animals like the Grylli, whose powers appear to com- 
mence nearly where ours terminate, may have the fac- 
ulty of hearing still sharper sounds which we do not 
know to exist, and that there may be other insects hear- 
ing nothing in common with us, but endowed with a 
power of exciting, and a sense which perceives vibrations 
of the same nature indeed as those which constitute our 
ordinary sounds, but so remote that the animals who 
perceive them may be said to possess another sense, 
agreeing with our own solely in the medium by which 
it is excited. 

M. Savart, so well known for the number and beauty 
of his researches in acoustics, has proved that a high 
note of a given intensity being heard by some ears and 
not by others, must not be attributed to its pitch, but to 
its feebleness. His experiments, and those more re- 
cently made by Professor Wheatstone, show, that if the 
pulses could be rendered sufficiently powerful, it would 
be difficult to fix a limit to human hearing at either end 
of the scale. M. Savart had a wheel made about nine 
inches in diameter with 360 teeth set at equal distances 
round its rim, so that while in motion each tooth suc- 
cessively hit on a piece of card. The tone increased in 
pitch with the rapidity of the rotation, and was very 
pure when the number of strokes did not exceed three 
or four thousand in a second, but beyond that it became 
feeble and indistinct. With a wheel of a larger size a 
much higher tone could be obtained, because the teeth 
being wider apart the blows were more intense and 
more separated from one another. With 720 teeth on 
a wheel thirty-two inches in diameter, the sound pro- 
duced by 12,000 strokes in a second was audible, which 
corresponds to 24,000 vibrations of a musical chord. So 
that the human ear can appreciate a sound which only 
lasts the 24,000th part of a second. This note was dis- 
tinctly heard by M. Savart and by several people who 
were present, which convinced him that with another 
apparatus still more acute sounds might be rendered 
audible. 

For the deep tones M. Savart employed a bar of iron, 
two feet eight inches long, about two inches broad, and 
half an inch in thickness, which revolved about its center 



SECT. XVI. VELOCITY OF SOUND. 127 

as if its arms were the spokes of a wheel. When such 
a machine rotates it impresses a motion on the air simi- 
lar to its own, and when a thin board or card is brought 
close to its extremities, the current of air is moment- 
arily interrupted at the instant each arm of 'the bar 
passes before the card ; it is compressed above the card 
and dilated below ; but the instant the spoke has passed, 
a rush of ah* to restore equilibrium makes a kind of ex- 
plosion, and when these succeed each other rapidly, a 
musical note is produced of a pitch proportional to the 
velocity of the revolution. When M. Savart turned this 
bar slowly a succession of single beats was heard ; as 
the velocity became greater the sound was only a rattle ; 
but as soon as it was sufficient to give eight beats in a 
second, a very deep musical note was distinctly audible, 
corresponding to sixteen single vibrations in a second, 
which is the lowest that has hitherto been produced. 
When the velocity of the bar was much increased the 
intensity of the sound was hardly bearable. The spokes 
of a revolving wheel produce the sensation of sound, on 
the very same principle that a burning stick whirled 
round gives the impression of a luminous circle. The 
vibrations excited in the organ of hearing by one beat 
have not ceased before another impulse is given. In- 
deed it is indispensable that the impressions made upon 
the auditory nerves should encroach upon each other in 
order to produce a full and continued note. On the 
whole, M. Savart has come to the conclusion, that the 
most acute sounds would be heard with as much ease 
as those of a lower pitch, if the duration of the sensation 
produced by each pulse could be diminished proportion- 
ally to the augmentation of the number of pulses in a 
given time : and on the contrary, if the duration of the 
sensation produced by each pulse could be increased in 
proportion to their number in a given time, that the 
deepest tones would be as audible as any of the others. 

The velocity of sound is uniform and independent of 
the nature, extent, and intensity of the primitive dis- 
turbance. Consequently sounds of every quality and 
pitch travel with equal speed. The smallest difference 
in their velocity is incompatible either with harmony or 
melody, for notes of different pitches and intensities 



128 VELOCITY OP SOUND SECT. XVI 

sounded together at a little distance, would arrive at the 
ear in different times. A rapid succession of notes 
would in this case produce confusion and discord. But 
as the rapidity with which sound is transmitted depends 
upon the elasticity of the medium through which it has 
to pass, whatever tends to increase the elasticity of the 
air must also accelerate the motion of sound. On that 
account its velocity is greater in warm than in cold 
weather, supposing the pressure of the atmosphere con- 
stant. In dry air at the freezing temperature, sound 
travels at the rate of 1090 feet in a second, and for any 
higher temperature one foot must be added for every 
degree of the thermometer above 32 ; hence at 62 of 
Fahrenheit its speed in a second is 1120 feet, or 765 
miles an hour, which is about three-fourths of the diur- 
nal velocity of the earth's equator. Since all the phe- 
nomena of the transmission of sound are simple conse- 
quences of the physical properties of the air, they have 
been predicted and computed rigorously by the laws of 
mechanics. It was found, however, that the velocity of 
sound determined by observation, exceeded what it ought 
to have been theoretically by 173 feet, or about one-sixth 
of the whole amount. La Place suggested that this dis- 
crepancy might arise from the increased elasticity of the 
air in consequence of a development of latent heat (N. 
173) during the undulations of sound, and calculation 
confirmed the accuracy of his views. The ae'rial mole- 
cules being suddenly compressed give out their latent 
heat ; and as air is too bad a conductor to carry it rap- 
idly off, it occasions a momentary and local rise of tem- 
perature which, increasing the elasticity of the air 
without at the same time increasing its inertia, causes 
the movement to be propagated more rapidly. Analysis 
gives the true velocity of sound in terms of the elevation 
of temperature that a mass of air is capable of commu- 
nicating to itself, by the disengagement of its own latent 
heat when suddenly compressed in a given ratio. This 
change of temperature however could not be obtained 
directly by any experiments which had been made at 
that epoch ; but by inverting the problem and assuming 
the velocity of sound as given by experiment, it was 
computed that the temperature of a mass of air is raised 



SICT. XVI. TRANSMISSION OF SOUND. 129 

nine-tenths of a degree when the compression is equal 
to j-} T of its volume. 

Probably all liquids are elastic, though considerable 
force is required to compress them. Water suffers a 
condensation of nearly 0-0000496 for every atmosphere 
of pressure, and is consequently capable of conveying 
sound even more rapidly than air, the velocity in the for- 
mer being 4708 feet in a second. A person under water 
hears sounds made in air feebly, but those produced in 
water very distinctly. According to the experiments of 
M. Colladon, the sound of a bell was conveyed under 
water through the Lake of Geneva to the distance of 
about nine miles. He also perceived that the progress 
of sound through water is greatly impeded by the inter- 
position of any object, such as a projecting wall ; conse- 
quently sound under water resembles light hi having a 
distinct shadow. It has much less in air, being trans- 
mitted all round buildings or other obstacles, so as te be 
heard in every direction, though often with a consid- 
erable diminution of intensity, as when a carriage turns 
the corner of a street. 

The velocity of sound in passing through solids is in 
proportion to their hardness, and is much greater than 
in air or water. A sound which takes some time in trav- 
eling through the air passes almost instantaneously along 
a wire six hundred feet long; consequently it is heard 
twice first as communicated by the wire and after- 
ward through the medium of the air. The facility 
with which the vibrations of sound are transmitted along 
the grain of a log of wood is well known. Indeed they 
pass through iron, glass, and some kinds of wood, at the 
rate of 18,530 feet in a second. The velocity of sound 
is obstructed by a variety of circumstances, such as fall- 
ing snow, fog, rain, or any other cause which disturbs 
the homogeneity of the medium through which it has 
to pass. M. de Humboldt says that it is on account of 
the greater homogeneity of the atmosphere during the 
night that sounds are then better heard than during the 
day, when its density is perpetually changing from par- 
tial variations of temperature. His attention was called 
to this subject on the plain surrounding the Mission of 
the Apures by the rushing noise of the great cataracts 
9 



130 TRANSMISSION OF SOUND. SECT. XVI. 

of the Oronoco, which seemed to be three times as loud 
by night as by day. This he illustrated by experiment. 
A tall glass half full of champaigne cannot be made to 
ring as long as the effervescence lasts. In order to pro- 
duce a musical note the glass together with the liquid it 
contains must vibrate in unison as a system, which it 
cannot do in consequence of the fixed air rising through 
the wine and disturbing its homogeneity, because the 
vibrations of the gas being much slower than those of 
the liquid the velocity of the sound is perpetually inter- 
rupted. For the same reason the transmission of sound 
as well as light is impeded in passing through an atmos- 
phere of variable density. Sir John Herschel, in his 
admirable Treatise on Sound, thus explains the phe- 
nomenon : "It is obvious," he says, "that sound as 
well as light must be obstructed, stifled, and dissipated 
from its original direction by the mixture of air of differ- 
ent temperatures, and consequently elasticities; and 
thus the same cause which produces that extreme 
transparency of the air at night, which astronomers 
alone fully appreciate, renders it also more favorable to 
sound. There is no doubt, however, that the universal 
and dead silence, generally prevalent at night, renders 
our auditory nerves sensible to impressions which would 
otherwise escape notice. The analogy between sound 
and light is perfect in this as in so many other respects. 
In the general light of day the stars disappear. In the 
continual hum of voices, which is always going on by 
day, and which reach us from all quarters and never 
leave the ear time to attain complete tranquillity, those 
feeble sounds which catch our attention at night make 
no impression. The ear, like the eye, requires long 
and perfect repose to attain its utmost sensibility." 

Many instances maybe brought in proof of the strength 
and clearness with which sound passes over the surface 
of water or ice. Lieutenant Foster was able to carry 
on a conversation across Fort Bowen harbor, when fro- 
zen, a distance of a mile and a half. 

The intensity of sound depends upon the extent of 
the excursions of the fluid molecules, on the energy of 
the transient condensations and dilatations, and on the 
greater or less number of particles which experience 



SMCT. XVI. INTENSITY OF SOUND. ]31 

these effects. We estimate that intensity by the im- 
petus of these fluid molecules on our organs, which is 
consequently as the square of the velocity, and not by 
their inertia, which is as the simple velocity. Were 
the latter the case there would be no sound, because the 
inertia of the receding waves of air would destroy .the 
equal and opposite inertia of those advancing ; whence 
it may be concluded that the intensity of sound dimin- 
ishes inversely as the square of the distance from its 
origin. In a tube, however, the force of sound does 
not decay as in open air, unless perhaps by friction 
against the sides. M. Biot found from a number of 
highly interesting experiments made on the pipes of the 
aqueducts in Paris, that a continual conversation could 
be carried on in the lowest possible whisper, through 
a cylindrical tube about 3120 feet long, the time of 
transmission through that space being 2-79 seconds. In 
most cases sound diverges in all directions so as to oc- 
cupy at any one time a spherical surface ; but Dr. Young 
has shown that there are exceptions, as for example 
when a flat surface vibrates only in one direction. The 
sound is then most intense when the ear is at right an- 
gles to the surface, whereas it is scarcely audible in a 
direction precisely perpendicular to its edge. In this 
case it is impossible that the whole of the surrounding 
air can be affected in the same manner, since the particles 
behind the sounding surface must be moving toward it, 
whenever the particles Before it are retreating. Hence 
in one half of the surrounding sphere of air its motions 
are retrogade, while in the other half they are direct ; 
consequently at the edges where these two portions 
meet, the motions of the air will neither be retrograde 
nor direct, and therefore it must be at rest. 

It appears from theory as well as daily experience, 
that sound is capable of reflection from surfaces (N. 174) 
according to the same laws as light. Indeed any one 
who has obs'erved the reflection of the waves from a 
wall on the side of a river after the passage of a steam- 
boat, will have a perfect idea of the reflection of sound 
and of light. As every substance in nature is more or 
less elastic, it may be agitated according to its own law 
by the impulse of a mass of undulating air ; and recip- 



132 ECHOES. SECT. XVI. 

rocally the surface by its reaction will communicate its 
undulations back again into the air. Such reflections 
produce echoes, and as a series of them may take place 
between two or more obstacles, each will cause an echo 
of the original sound, growing fainter and fainter till it 
dies away ; because sound, like light, is weakened by 
reflection. Should the reflecting surface be concave 
toward a person, the sound will converge toward him 
with increased intensity, which will be greater still if 
the surface be spherical and concentric with him. Un- 
dulations of sound diverging from one focus of an ellip- 
tical shell (N. 175) converge in the other after reflec- 
tion. Consequently a sound from the one will be heard 
in the other as if it were close to the ear. The rolling 
noise of thunder has been attributed to reverberation 
between different clouds, which may possibly be the 
case to a certain extent. Sir John Herschel is of opin- 
ion, that an intensely prolonged peal is probably owing 
to a combination of sounds because the velocity of elec- 
tricity being incomparably greater than that of sound, 
the thunder may be regarded as originating in every 
point of a flash of lightning at the same instant. The 
sound from the nearest point will arrive first, and if the 
flash run in a direct line from a person, the noise will 
come later and later from the remote points of its path 
in a continued roar. Should the direction of the flash 
be inclined, the succession of sounds will be more rapid 
and intense, and if the lightning describe a circular curve 
round a person, the sound will arrive from every point 
at the same instant with a stunning crash. In like 
manner the subterranean noises heard during earth- 
quakes like distant thunder, may arise from the conse- 
cutive arrival at the ear of undulations propagated at the 
same instant from nearer and more remote points ; or 
if they originate in the same point, the sound may 
come by different routes through strata of different den- 
sities. 

Sounds under water are heard very distinctly in the 
air immediately above ; but the intensity decays with 
great rapidity as the observer goes farther off, and is 
altogether inaudible at the distance of two or three 
hundred yards. So that waves of sound, like those of 



- * 

SKCT. XVI. INTERFERENCE OF SOUNDS. 133 

light, in passing from a dense to a rare medium, are not 
only refracted, but suffer total reflection at veiy oblique 
incidences (N. 184). 

The laws of interference extend also to sound. It is 
clear that two equal and similar musical strings will be 
in unison, if they communicate the same number of 
vibrations to the air in the same time. But if two such 
stiings be so nearly in unison, that one performs a hun- 
dred vibrations in a second, and the other a hundred 
and one in the same period during the first few vibra- 
tions, the two resulting sounds will combine to form one 
of double the intensity of either, because the aerial waves 
will sensibly coincide in time and place ; but one will 
gradually gain on the other till at the fiftieth vibration it 
will be half an oscillation in advance. Then the waves 
of air which produce the sound being sensibly equal, but 
the receding part of the one coinciding with the advan- 
cing part of the other, they will destroy one another and 
occasion an instant of silence. The sound will be re- 
newed immediately after, and will gradually increase 
till the hundredth vibration, when the two waves will 
combine to produce a sound double the intensity of either. 
These intervals of silence and greatest intensity, called 
beats, will recur every second ; but if the notes differ 
much from one another the alternations will resemble a 
rattle ; and if the strings be in perfect unison there will 
be no beats, since there will be no interference. Thus 
by interference is meant the coexistence of two undula- 
tions in which the lengths of the waves are the same. 
And as the magnitude of an undulation may be dimin- 
ished by the addition of another transmitted in the same 
direction, it follows that one undulation may be abso- 
lutely destroyed by another when waves of the same 
length are transmitted in the same direction, provided 
that the maxima of the undulations are equal, and that 
one follows the other by half the length of a wave. A 
tuning-fork affords a good example of interference. 
When that instrument vibrates, its two branches alter- 
nately recede from and approach one another ; ach 
communicates its vibrations to the ah*, and a musical 
note is the consequence. If the fork be held upright, 
about a foot from the ear, and turned round its axis while 
M 



134 VIBRATION OF MUSICAL STRINGS. SECT. XVII. 

vibrating, at every quarter revolution the sound will 
scarcely be heard, while at the intermediate points it 
will be strong and clear. This phenomenon arises 
from the interference of the undulations of air coming 
from the two branches of the fork. When the two 
branches coincide, or when they are at equal distances 
from the ear, the waves of air combine to reinforce each 
other ; but at the quadrants, where the two branches 
are at unequal distances from the ear, the lengths of the 
waves differ by half an undulation, and consequently 
destroy one another. 



SECTION XVII. 

Vibration of Musical String's Harmonic Sounds Nodes Vibration of Air 
in Wind Instruments Vibration of Solids Vibrating Plates Bells- 
Harmony Sounding Boards Forced Vibrations Resonance Speaking 
Machines. 

WHEN the particles of elastic bodies are suddenly 
disturbed by an impulse, they return to their natural 
position by a series of isochronous vibrations, whose 
rapidity, force, and permanency depend upon the elas- 
ticity, the form, and the mode of aggregation which 
unites the particles of the body. These oscillations are 
communicated to the air, and on account of its elasticity 
they excite alternate condensations and dilatations in 
the strata of the fluid nearest to the vibrating body : 
from thence they are propagated to a distance. A string 
or wire stretched between two pins, when drawn aside 
and suddenly let go, will vibrate till its own rigidity and 
the resistance of the air reduce it to rest. These oscil- 
lations may be rotatory in every plane, or confined to one 
plane, according as the motion is communicated. In the 
piano-forte, where the strings are struck by a hammer 
at one extremity, the vibrations probably consist of a 
bulge running to and fro from end to end. Different 
modes of vibration may be obtained from the same so- 
norous body. Suppose a vibrating string to give the 
lowest C of the piano-forte, which is the fundamental 
note of the string ; if it be lightly touched exactly in the 
middle so as to retain that point at rest, each half will 



SKCT. XVII. VIBRATION OP MUSICAL STRINGS. 135 

then vibrate twice as fast as the whole, but in opposite 
directious ; the ventral or bulging segments will be alter- 
nately above and below the natural position of the string, 
and the resulting note will be the octave above C. When 
a point at a third of the length of the string is kept at 
rest, the vibrations will be three times as fast as those 
of the whole string, and will give the twelfth above C. 
When the point of rest is one fourth of the whole, the 
oscillations will be four times as fast as those of the fun- 
damental note, and will give the double octave ; and so 
on. These acute sounds are called the harmonics of 
the fundamental note. It is clear from what has been 
stated, that the string thus vibrating could not give these 
harmonics spontaneously unless it divided itself at its 
aliquot parts into two, three, four, or more segments in 
opposite states of vibration separated by points actually 
at rest. In proof of this, pieces of paper placed on the 
string at the half, third, fouith, or other aliquot points 
according to the corresponding harmonic sound, will re- 
main on it during its vibration, but will instantly fly off 
from any of the intermediate points. The po.ints of 
rest called the nodal points of the string, are a mere 
consequence of the law of interferences. For if a rope 
fastened at one end be moved to and fro at the other 
extremity so as to transmit a succession of equal waves 
along it, they will be successively reflected when they 
arrive at the other end of the rope by the fixed point, 
and in returning they will occasionally interfere with 
the advancing waves ; and as these opposite undulations 
will at certain points destroy one another, the point of 
the rope in which this happens will remain at rest. 
Thus a series of nodes and ventral segments will be 
produced, whose number will depend upon the tension 
and the frequency of the alternate motions communi- 
cated to the movable end. So when a string fixed at 
both ends is put in motion by a sudden blow at any^oint 
of it, the primitive impulse divides itself into two pulses 
running opposite ways, which are each totally reflected 
at the extremities, and running back again along the 
whole length are again reflected at the other ends. And 
thus they will continue to run backward and forward, 
crossing one another at each traverse, and occasionally 



136 HARMONIC SOUNDS. SECT. XVII. 

interfering, so as to produce nodes ; so that the motion 
of a string fastened at both ends consists of a wave or 
pulse, continually doubled back on itself by reflection at 
the fixed extremities. 

Harmonics generally coexist with the fundamental 
sound in the same vibrating body. If one of the lowest 
strings of the piano-forte be struck, an attentive ear 
will not only hear the fundamental note, but will detect 
all the others sounding along with it, though "with less 
and less intensity as their pitch becomes higher. Ac- 
cording to the law of coexisting undulations, the whole 
string and each of its aliquot parts are in different and 
independent states of vibration at the same time ; and 
as all the resulting notes are heard simultaneously, not 
only the air but the ear also vibrates in unison with 
each at the same instant (N. 176). 

Harmony consists in an agreeable combination of 
sounds. When two chords perform their vibrations in 
the same time, ttjey are in unison. But when their 
vibrations are so related as to have a common period 
after a few oscillations they produce concord. Thus 
when the vibrations of two strings bear a very simple 
relation to each other, as where one of them makes 
two, three, four, &c. vibrations in the time the other 
makes one ; or if it accomplishes three, four, &c. vibra- 
tions while the other makes two, the result is a concord 
which is the more perfect the shorter the common 
period. In discords, on the contrary, the beats are 
distinctly audible, which produces a disagreeable and 
harsh effect, because the vibrations do not bear a simple 
relation to one another, as where one of two strings 
makes eight vibrations while the other accomplishes 
fifteen. The pleasure afforded by harmony is attributed 
by Dr. Young to the love of order, and to a predilection 
for a regular repetition of sensations natural to the 
human mind, which is gratified by the perfect regularity 
and rapid recurrence of the vibrations. The love of 
poetry and dancing he conceives to aris,e in some degree 
from the rhythm of the one and the regularity of the 
motions in the other. 

A blast of air passing over the open end of a tube, as 
over the reeds in Pan's pipes ; over a hole in one side, 



SECT. XVII. VIBRATION OF A COLUMN OF AIR. 137 

as in the flute ; or through the aperture called a reed 
with a flexible tongue, as in the clarinet, puts the inter- 
nal column of air into longitudinal vibrations by the 
alternate condensations and rarefactions of its particles. 
At the same time the column spontaneously divides 
itself into nodes between which the air also vibrates 
longitudinally, but with a rapidity inversely proportional 
to the length of the divisions, giving the fundamental 
note or one of its harmonics. The nodes are produced 
on the principle of interferences by the reflection of the 
longitudinal undulations of the air at the ends of the 
pipe, as in the musical string, only that in one case the 
undulations are longitudinal, and in the other transverse. 
A pipe either open or shut at both ends when 
sounded vibrates entire, or divides itself spontaneously 
into two, three, four, &c. segments separated by nodes. 
The whole column gives the fundamental note by 
waves or vibrations of the same length with the pipe. 
The first harmonic is produced by waves half as lon as 
the tube, the second harmonic by waves a third as long, 
and so on. Th^ harmonic segments in an open and 
shut pipe are the same in number, but differently 
placed. In a shut pipe the two ends are nodes, but in 
an open pipe there is half a segment at each extremity, 
because the air at these points is neither rarefied nor 
condensed, being in contact with that which is external. 
If one of the ends of the open pipe be closed, its funda- 
mental note will be an octave lower, the air will now 
divide itself into three, five, seven, &c. segments ; and 
the wave producing its fundamental note will be twice 
as long as the pipe, so that it will be doubled back 
(X. 177). All these notes may be produced separately, 
by varying the intensity of the blast. Blowing steadily 
and gently, the fundamental note will sound ; when the 
force of the blast is increased, the note will all at once 
start up an octave ; when the intensity of the wind is 
augmented, the twelfth will be heard, and by continuing 
to increase the force of the blast the other harmonics 
may be obtained, but no force of wind will produce a 
note intermediate between these. The harmonics of a 
flute may be obtained in this manner, from the lowest 
C or D upward, without altering the fingering, merely 
M 2 



138 VIBRATION OF SPRINGS AND RODS. SECT. XVII. 

by increasing the intensity of the blast, and altering the 
form of the lips. Pipes of the same dimensions, 
whether of lead, glass, or wood, give the same tone as to 
pitch under the same circumstances, which shows that 
the air alone produces the sound. 

Metal springs fastened at one end, when forcibly 
bent, endeavor to return to rest by a series of vibrations, 
which give very pleasing tones, as in musical boxes. 
Various musical instruments have recently been con- 
structed, consisting of metallic springs thrown into vibra- 
tion by a current of air. Among the most perfect of these 
are Mr. Wheatstone's Symphonion, Concertina, and JE>o- 
lian Organ, instruments of different effects and capabilities, 
but all possessing considerable execution and expression. 

The Syren is an ingenious instrument, devised by M. 
Cagniard de la Tour, for ascertaining the number of 
pulsations in a second corresponding to each pitch : the 
notes are produced by jets of air passing through small 
apertures arranged at regular distances in a circle on 
the side of a box, before which a disc Devolves pierced 
with the same number of holes. During a revolution 
of the disc the currents are alternately intercepted and 
allowed to pass as many times as there are apertures ir 
it, and a sound is produced whose pitch depends on the 
velocity of rotation. 

A glass or metallic rod, when struck at one end, or 
rubbed in the direction of its length with a wet finger, 
vibrates longitudinally like a column of air, by the alter- 
nate condensation and expansion of its constituent par- 
ticles, producing a clear and beautiful musical note of 
a high pitch, on account of the rapidity with which 
these substances transmit sound. Rods, surfaces, and, 
in genera], all, undulating bodies, resolve themselves into 
nodes. But in surfaces, the parts which remain at rest 
during their vibrations are lines, which are curved or 
plane according to the substance, its form, and the mode 
of vibration. If a little fine dry sand be strewed over 
the surface of a plate of glass or metal, and if undula- 
tions be excited by drawing the bow of a violin across 
its edge, it will emit a musical sound, and the sand 
will immediately arrange itself in the nodal lines, where 
alone it will accumulate and remain at rest, because the 



Seer. XVII. VIBRATION OF PLATES. 139 

segments of the surface on each side will be in different 
states of vibration, the one being elevated while the 
other is depressed ; and as these two motions meet in 
the nodal lines, they neutralize one another. These 
lines vary in form and position with the part where the 
bow is drawn across, and the point by which the plate 
is held. The motion of the sand shows in what direc- 
tion the vibrations take place. If they be perpendicular 
to the surface, the sand will be violently tossed up and 
down, till it finds the points of rest. If they be tan- 
gential, the sand will only creep along the surface to 
the nodal lines. Sometimes the undulations are oblique, 
or compounded of both the preceding. If a bow be 
drawn across one of the angles of a square plate of glass 
or metal held firmly by the center, the sand will ar- 
range itself in two straight lines parallel to the sides of 
the plate, and crossing in the center so as to divide it 
into four equal squares, whose motions will be contrary 
to each other. Two of the diagonal squares will make 
their excursions on one side of the plate, while the 
other two make their vibrations on the other side of it. 
This mode of vibration produces the lowest tone of the 
plate (N. 178). If the plate be still held by the center, 
and the bow applied to the middle of one of the sides, 
the vibrations will be more rapid, and the tone will be a 
fifth higher than in the preceding case ; now the sand 
will arrange itself from corner to corner, and will divide 
the plate into four equal triangles, each pair of which 
will make their excursions on opposite sides of the 
plate. The nodal lines and pitch vary not only with 
the point where the bow is applied, but with the point 
by which the plate is held, which being at rest, neces- 
sarily determines the direction of one of the quiescent 
lines. The forms assumed by the sand in square 
plates are very numerous, corresponding to all the va- 
rious modes of vibration. The lines in circular plates 
are even more remarkable for their symmetry, and 
upon them the forms assumed by the sand may be 
classed in three systems. The first is the diametrical 
system, in which the figures consist of diameters divid- 
ing the circumference of the plate into equal parts, 
ench of which is in a different state of vibration from 



140 VIBRATION OF PLATES. SECT. XVII. 

those adjacent. Two diameters, for example, crossing 
at right angles, divide the circumference into four equal 
parts ; three diameters divide it into six equal parts ; 
four divide it into eight, and so on. In a metallic plate, 
these divisions may amount to thirty-six or forty. The 
next is the concentric system, where the sand arranges 
itself in circles, having the same center with the plate ; 
and the third is the compound system, where the figures 
assumed by the sand are compounded of the other two, 
producing veiy complicated and beautiful forms. Ga- 
lileo seems to have been the first to notice the points of 
rest and motion in the sounding-board of a musical 
instrument ; but to Chladni is due the whole discovery 
of the symmetrical forms of the nodal lines in vibrating 
plates (N. 179). Professor Wheatstone has shown in 
a paper read before the Royal Society, in 1833, that all 
Chladni' s figures, and indeed all the nodal figures of 
vibrating surfaces, result from very simple modes of 
vibration, oscillating isochronously, and superposed upon 
each other ; the resulting figure varying with the com- 
ponent modes of vibration, the number of the super- 
positions, and the angles at which they are superposed. 
For example, if a square plate be vibrating so as to make 
the sand arrange itself in straight lines parallel to one 
side of the plate, and if, in addition to this, such vibra- 
tions be excited as would have caused the sand to form 
in lines perpendicular to the first had the plate been 
at rest, the combined vibrations will make the sand form 
in lines from corner to corner (N. 180). 

M. Savait's experiments on the vibrations of flat glass 
rulers are highly interesting. Let a lamina of glass 
27 in -56 long, 0-59 of an inch broad, 0-06 of an inch in 
thickness, be held by the edges in the middle, with its 
flat surface horizontal. If this surface be strewed with 
sand, and set in longitudinal vibration by rubbing its 
under surface with a wet cloth, the sand on the upper 
surface will arrange itself in lines parallel to the ends of 
the lamina, always in one or other of two systems 
(N. 181). Although the same one of the two systems 
will always be produced by the same plate of glass, yet 
among different plates of the preceding dimensions, even 
though cut from the same sheet side by side* one will 



SJCCT. XVII. VIBRATION OP LAMINJE. 14J 

invariably exhibit one system, and the other the other, 
without any visible reason for the difference. Now if 
the positions of these quiescent lines be marked on the 
upper surface, and if the plate be turned so that the 
lower surface becomes the upper one, the sand being 
strewed, and vibrations excited 33 before, the nodal lines 
will still be parallel to the ends of the lamina, but their 
positions will be intermediate between those of the 
upper surface (N. 182). Thus it appears that all the 
motions of one half of the thickness of the lamina, or 
ruler, are exactly contrary to those of the corresponding 
points of the other half. If the thickness of the lamina 
be increased, the other dimensions remaining the same, 
the sound will not vary, but the number of nodal lines 
will be less. When the breadth of the lamina exceeds 
the 0-6 of an inch, the nodal lines-become curved and are 
different on the two surfaces. A great variety of forms 
are produced by increasing the breadth and changing 
the form of the surface ; but in all, it appears that the 
motions in one half of the thickness are opposed to those 
in the other half. 

M. Savart also found, by placing small paper rings 
round a cylindrical tube or rod, so as to rest upon it at 
one point only, that when the tube or rod is continually 
turned on its axis in the same direction, the rings slide 
along during the vibrations, till they come to a quiescent 
point, where they rest. By tracing these nodal lines he 
discovered that they twist in a spiral or corkscrew round 
rods and cylinders, making one or more turns according 
to the length ; but at certain points, varying in number 
according to the mode of vibration of the rod, the screw 
stops, and recommences on the other side, though it is 
turned in a contraiy direction ; that is, on one side it is 
a right-handed screw, on the other a left (N. 183). The 
nodal lines in the interior surface of the tubes are per- 
fectly similar to those in the exterior, but they occupy 
intermediate positions. If a small ivory ball be put 
within the tube, it will follow these nodal lines when 
the tube is made to revolve on its axis. 

AH solids which ring when struck, such as bells, 
drinking glasses, gongs, &c., have their shape momen- 
tarily and forcibly changed by the blow, and from their 



142 SYMPATHETIC VIBRATION. SECT. XVII 

elasticity, or tendency to resume their natural form, a 
series of undulations takes place, owing to the alternate 
condensations and rarefactions _of the particles of solid 
matter. These have also their harmonic tones, and 
consequently nodes. Indeed generally, when a rigid 
system of any form whatever vibrates either transverse- 
ly or longitudinally, it divides itself into a certain number 
of parts, which perform their vibrations without disturb- 
ing one another. These parts are at eveiy instant in 
alternate states of undulation ; and as the points or lines 
where they join partake of both they remain at rest, 
because the opposing motions destroy one another. 

The air, notwithstanding its rarity, is capable of trans- 
mitting its undulations when in contact with a body sus- 
ceptible of admitting and exciting them. It is thus that 
sympathetic undulations are excited by a body vibrating 
near insulated tended strings, capable of following its 
undulations, either by vibrating entire, or by separating 
themselves into their harmonic divisions. If two chords 
equally stretched, of which one is twice or three times 
longer than the other, be placed side by side, and if the 
shorter be sounded, its vibrations will be communicated 
by the air to the other, which will be thrown into such 
a state of vibration that it will be spontaneously divided 
into segments equal in length to the shorter string. 
When a tuning-fork receives a blow and is made to rest 
upon a piano-forte during its vibration, every string 
which, either by its natural length or by its spontaneous 
subdivisions, is capable of executing corresponding vibra- 
tions, responds in a sympathetic note. Some one or 
other of the notes of an organ are generally in unison 
with one of the panes or with the whole sash of a win- 
dow, which consequently resounds when these notes 
are sounded. A peal of thunder has frequently the 
same effect. The sound of very large organ-pipes is 
generally inaudible till the air be set in motion by the 
undulations of some of the superior accords, and then 
its sound becomes extremely energetic. Recurring vi- 
brations occasionally influence each other's periods. For 
example, two adjacent organ-pipes nearly in unison, may 
force themselves into concord ; and two clocks whose 
rates differed considerably when separate, have been 



S*cr. XVII. VIBRATION OF PAPER AND VELLUM. 143 

known to beat together when fixed to the same wall, 
and one clock has forced the pendulum of another into 
motion, when merely standing on the same stone pave- 
ment. These forced, oscillations, which correspond in 
their periods with those of the exciting cause, are to be 
traced in every department of physical science. Several 
instances of them have already occurred in this work. 
Such are the tides, which follow the sun and moon in all 
their motions and,periods. The nutation of the earth's 
axis also, which corresponds with the period, and repre- 
sents the motion of the nodes of the moon, is again 
reflected back to the moon, and may be traced in the 
nutation of the 1 lunar orbit. And lastly, the acceleration 
of the moon's mean motion represents the action of the 
planets on the earth reflected by the sun to the moon. 

In consequence of the facility with which the air 
communicates undulations, all the phenomena of vibrat- 
ing plates may be exhibited by sand strewed on paper or 
parchment, stretched over a harmonica glass or large 
bell-shaped tumbler. In order to give due tension to 
the paper or vellum, it must be wetted, stretched over 
the glass, gummed round the edges, allowed to dry, and 
varnished over to prevent changes in its tension from the 
humidity of the atmosphere. If a circular disc of glass 
be held concentrically over this apparatus, with its plane 
parallel to the surface of the paper, and set in vibration 
by drawing a bow across its edge, so as to make sand on 
its surface take any of Chladni's figures, the sand on the 
paper will assume the very same form, in consequence 
of the vibrations of the disc being communicated to the 
paper by the air. When the disc is removed slowly in 
a horizontal direction, the forms on the paper will cor- 
respond with those on the disc, till the distance is too 
great for the air to convey the vibrations. If the disc 
while vibrating be gradually more and more inclined to 
the horizon, the figures on the paper will vary by de- 
grees; and when the vibrating disc is perpendicular to 
the horizon, the sand on the paper will form into straight 
lines parallel to the surface oT the disc, by creeping along it 
instead of dancing up and down. If the disc be made to 
turn round its vertical diameter while vibrating, the nodal 
lines on the paper will revolve, and exactly follow the 



144 NODAL LINES IN AtR. SECT. XVII. 

motion of the disc. It appears from this experiment, 
that the motions of the aerial molecules in every part of 
a spherical wave, propagated from a vibrating body as a 
center, are parallel to each other, and not divergent like 
the radii of a circle. When a slow air is played on a 
flute near this apparatus, each note calls up a particular 
form in the sand, which the next note effaces to estab- 
lish its own. The motion of the sand will even detect 
Bounds that are inaudible. By the vibrations of sand on 
a drum-head the besieged have discovered the direction 
in which a counter-mine was working. M. Savart, who 
made these beautiful experiments, employed this appa- 
ratus to discover nodal lines in masses of air. He found 
that the air of a room, when thrown into undulations by 
the continued sound of an organ-pipe, or by any other 
means, divides itself into masses separated by nodal 
curves of double curvature, such as spirals, on each side 
of which the air is in opposite states of vibration. He 
even traced these quiescent lines going out at an open 
window, and for a considerable distance in the open air. 
The sand is violently agitated where the undulations of 
the air are greatest, and remains at rest in the nodal 
lines. M. Savart observed, that when he moved his 
head away from a quiescent line toward the right the 
sound appeared to come from the right, and when he 
moved it toward the left the sound seemed to come from 
the left, because the molecules of air are in different 
states of motion on each side of the quiescent line. 

A musical string gives a very feeble sound when vi- 
brating alone, on account of the small quantity of air set 
in motion. But when attached to a sounding-board, as 
in the harp and piano-forte, it communicates its undula- 
tions to that surface, and from thence to every part of 
the instrument ; so that the whole system vibrates iso- 
chronously, and by exposing an extensive undulating sur- 
face, which transmits its undulations to a great mass of 
air, the sound is much reinforced. The intensity is 
greatest when the vibrations of the string or sounding 
body are perpendicular to the sounding-board, and least 
when they are in the same plane with it. The sound- 
ing-board of the piano-forte is better disposed than that 
of any other stringed instrument, because the hammers 



SECT. XVII. RESONANCE. 145 

strike the strings so as to make them vibrate at right 
angles to it. In the guitar, on the contrary, they are 
struck obliquely, which renders the tone feeble, unless 
when the sides, which also act as a sounding-board, are 
deep. It is evident that the sounding-board and the 
whole instrument are agitated at once by all the super- 
posed vibrations excited by the simultaneous or consecu- 
tive notes that are sounded, each having its perfect effect 
independently of the rest.. A sounding-board not only 
reciprocates the different degrees of pitch, but all the 
nameless qualities of tone. This has been beautifully 
illustrated by Professor Wheatstone in a series of exper- 
iments on the transmission through solid conductors of 
musical performances, from the harp, piano, violin, clar- 
inet, &c. He found that all the varieties of pitch, qual- 
ity, and intensity, are perfectly transmitted with their 
relative gradations, and may be communicated through 
conducting wires or rods of very considerable length, to 
a properly disposed sounding-board in a distant apart- 
ment. The sounds of an entire orchestra may be trans- 
mitted and reciprocated by connecting one end of a 
metallic rod with a sounding-board near tbe orchestra, 
so placed as to resound to all the instruments, and the 
other end with the sounding-board of a harp, piano, or 
guitar, in a remote apartment. Professor Wheatstone 
observes, "The effect of this experiment is very pleas- 
ing; the sounds, indeed, have so little intensity as scarcely 
to be heard at a distance from the reciprocating instru- 
ment ; but on placing the ear close to it, a diminutive 
band is heard, in which all the instruments preserve 
their distinctive qualities, and the pianos and fortes, the 
crescendos and diminuendos, their relative contrasts. 
Compared with an ordinary band heard at a distance 
through the air, the effect is as a landscape seen in min- 
iature beauty through a concave lens, compared with 
the same scene viewed by ordinary vision through a 
murky atmosphere." 

Every one is aware of the reinforcement of sound by 
the resonance of cavities. When singing or speaking 
near the aperture of a wide-mouthed vessel, the inten- 
sity of some one note in unison with the air in the cav- 
ity, is often augmented to a great degree. A.ny vessel 
10 N 



146 RESONANCE. SECT. XVII. 

will resound if a body vibrating the natural note of the 
cavity be placed opposite to its orifice, and be large 
enough to cover it ; or at least to set a large portion of 
the adjacent air in motion. For the sound will be alter- 
nately reflected by the bottom of the cavity and the un- 
dulating body at its mouth. The first impulse of the 
undulating substance will be reflected by the bottom of 
the cavity, and then by the undulating body, in time to 
combine with the second new impulse. This reinforced 
sound will also be twice reflected in time to conspire 
with the third new impulse ; and as the same process 
will be repeated on every new impulse, each will com- 
bine with all its echoes to reinforce the sound pro- 
digiously. Professor Wheatstone, to whose ingenuity 
we are indebted for so much new and valuable informa- 
tion on the theory of sound, has given some veiy striking 
instances of resonance. If one of the branches of a vi- 
brating tuning-fork be brought near the embouchure of 
a, flute, the lateral apertures of which are stopped so as 
to render it capable of producing the same sound as the 
fork, the feeble and scarcely audible sound of the fork 
will be augmented by the rich resonance of the column 
of air within the flute, and the tone will be full and clear. 
The sound will be found greatly to decrease by closing 
or opening another aperture ; for the alteration in the 
length of the column of air renders it no longer fit per- 
fectly to reciprocate the sound of the fork. This exper- 
iment may be made on a concert flute with a C tuning- 
fork. But Professor Wheatstone observes, that in this 
case it is generally necessary to finger the flute for B, 
because when blown into with the mouth the under-lip 
partly covers the embouchure, which renders the sound 
about a semitone flatter than it would be were the em- 
bouchure entirely uncovered. He has also shown, by 
the following experiment, that any one among several 
simultaneous sounds may be rendered separately audible. 
If two bottles be selected, and tuned by filling them with 
such a quantity of water as will render them unisonant 
with two tuning-forks which differ in pitch, on bringing 
both of the vibrating tuning-forks to the mouth of each 
bottle alternately, in each case that sound only will be 
heard which is reciprocated by 'the unisonant bottle. 



SICT. XVIII. A SPEAKING MACHINE. 147 

Several attempts have been made to imitate the artic- 
ulation of the letters of the alphabet. About the year 
1779, MM. Kratzenstein of St. Petersburgh, and Kem- 
pelen of Vienna, constructed instruments which articu- 
lated many letters, words, and even sentences. Mr. 
Willis of Cambridge has recently adapted cylindrical 
tubes to a reed, whose length can be varied at pleasure 
by sliding joints. Upon drawing out a tube while a col- 
umn of air from the bellows of ah organ is passing 
through it, the vowels are pronounced in the order, 2, 6, 
a, o, u. On extending the tube they are repeated after 
a certain interval, in the inverted order, u, o y a, c, i. Af- 
ter another interval they are flgain obtained in the direct 
order, and so on. When the pitch of the reed is very 
high, it is impossible to sound some of the vowels, which 
is in perfect correspondence with the human voice, fe- 
male singers being unable to pronounce u and o in their 
high notes. From the singular discoveries of M. Savart 
on the nature of the human voice, and the investiga- 
tions of Mr. Willis on the mechanism of the larynx, 
it may be presumed that ultimately the utterance- or 
pronunciation of mod ern*langu ages will be conveyed, 
not only to the eye but also to the ear of posterity. 
Had the ancients possessed the means of transmitting 
such definite sounds, the civilized world would ^till have 
responded in sympathetic notes at the distance of many 
ages. 



SECTION XVIII. 

Refraction Astronomical Refraction and its Laws Formation of Tables of 
Refraction Terrestrial Refraction Its Quantity Instances of Extraor- 
dinary Refraction Reflection Instances of Extraordinary Reflection 
Loss of Light by the Absorbing Power of the Atmosphere Apparent 
Magnitude of Sun and Moon in the Horizon. 

NOT only everything we hear but all we see is through 
the medium of the atmosphere. Without some knowl- 
edge of its action upon light, it would be impossible to 
ascertain the position of the heavenly bodies, or even to 
determine the exact place of very distant objects upon 
the surface of the earth ; for in consequence of the re- 



148 ASTRONOMICAL REFRACTION. SECT. XVIII. 

Tractive power of the air, no distant object is seen in its 
true position. 

All the celestial bodies appear to be more elevated 
than they really are ; because the rays of light, instead 
of moving through the atmosphere in straight lines, are 
continually inflected toward the earth. Light passing 
obliquely out of a rare into a denser medium, as from 
vacuum into air, or from air into water, is bent or re- 
fracted from its course toward a perpendicular to that 
point of the denser surface where the light enters it 
(N. 184). In the same medium, the sine of the angle 
contained between the incident ray and the perpendic- 
ular is in a constant ratio to the sine of the angle con- 
tained by the refracted ray and the same perpendicu- 
lar ; but this ratio varies with the refracting medium. 
The denser the medium the more the ray is bent. 
The barometer shows that the density of the atmos- 
phere decreases as the height above the earth increases. 
Direct experiments prove that the refractive power of 
the air increases with its density. It follows therefore 
that if the temperature be uniform, the refractive power 
of the air is greatest at the earth's surface and dimin- 
ishes upward. 

A ray of light from a celestial object falling obliquely 
on this variable atmosphere, instead of being refracted 
at once from its course, is gradually more and more bent 
during its passage through it so as to move in a vertical 
curved line, in the same manner as if the atmosphere 
consisted of an infinite number of strata of different den- 
sities. The object is seen in the direction of a tangent 
to that part of the curve which meets the eye, conse- 
quently the apparent altitude (N. 185) of the heavenly 
bodies is always greater than their true altitude. Owing 
to this circumstance, the stars are seen above the hori- 
zon after they are set, and the day is lengthened from 
a part of the sun being visible, though he really is behind 
the rotundity of the earth. It would be easy to de- 
termine the direction of a ray of light through the at- 
mosphere if the law of the density were known ; but as 
this law is perpetually varying with the temperature, 
the case is very complicated. When rays pass perpen- 
dicularly from one medium into another, they are not 



SECT. XVIII. ASTRONOMICAL REFRACTION. 149 

bent ; and experience shows, that in the same surface, 
though the sines of the angles of incidence and refrac- 
tion retain the same ratio, the refraction increases with 
the obliquity of incidence (N. 184). Hence it appears 
that the refraction is greatest at the horizon, and at the 
zenith there is none. But it is proved that at all heights 
above ten degrees, refraction varies nearly as the tangent 
of the angular distance of the object from the zenith, 
and wholly depends upon the heights of the barometer 
and thermometer. For the quantity of refraction at the 
same distance from the zenith varies nearly as the height 
of the barometer, the temperature being constant; and 
the effect of the variation of temperature is to diminish 
the quantity of refraction by about its 480th part for 
every degree in the rise of Fahrenheit's thermometer. 
Not much reliance can be placed on celestial observa- 
tions, within less than ten or twelve degrees of the 
horizon, on account of irregular variations in the density 
of the air near the surface of the earth, which are 
sometimes the cause of very singular phenomena. The 
humidity of the ah' produces no sensible effect on its 
refractive power. 

Bodies, whether luminous or not, are only visible by 
the rays which proceed from them. As the rays must 
pass through strata of different densities in coming to us, 
it follows that with the exception of stars in the zenith, 
no object either in or beyond our atmosphere is seen in 
its true place. But the deviation is so smalHp ordinary 
cases that it causes no inconvenience, though in astro- 
nomical and trigonometrical observations diie allowance 
must be made for the effects of refraction. Dr. Brad- 
ley's tables of refraction were formed by observing the 
zenith distances of the sun at his greatest declinations, 
and the zenith distances of the pole-star above and below 
the pole. The sum of these four quantities is equal to 
180, diminished by the sum of the four refractions, 
whence the sum of the four, refractions was obtained ; 
and from the law of the variation of refraction determined 
by theory, he assigned the quantity due to each altitude 
(N. 186). The mean horizontal refraction is about 
35' 6", and at the height of forty-five degrees it is 58"-36. 
The effect of refraction upon the same star above and 



150 TERRESTRIAL REFRACTION. SECT. XVIII. 

below the pole was noticed by Alhazen, a Saracen 
astronomer of Spain, in' the ninth century, but its exis- 
tence, was known to Ptolemy in the second, though he 
was ignorant of its quantity. 

The refraction of a terrestrial object is estimated dif- 
ferently from that of a celestial body. It is measured 
by the angle contained between the tangent to the 
curvilineal path of the ray where it meets the eye, and 
the straight line joining the eye and the object (N. 187). 
Near the earth's surface the path of the ray may be 
supposed to be circular ; and the angle at the center of 
the earth corresponding to this path is called the hori- 
zontal angle. The quantity of terrestrial refraction is 
obtained by measuring contemporaneously the elevation 
of the top of a mountain above a point in the plain at its 
base, and the depression of that point below the top of 
the mountain. The distance between these two sta- 
tions is the chord of the horizontal angle ; and it is easy 
to prove that double the refraction is equal to the 
horizontal angle, increased by the difference between 
the apparent elevation and 4he apparent depression. 
Whence it appears that in the mean state of the atmos- 
phere, the refraction is about the fourteenth part of the 
horizontal angle. 

Some very singular appearances occur from the acci- 
dental expansion or condensation of the strata of the 
atmosphere contiguous to the surface of the earth, by 
which distant objects, instead of being elevated, are de- 
pressed. Sometimes being at once both elevated and 
depressed they appear double, one of the images being 
direct, and the other inverted.. In consequence of the 
upper edges of the sun and moon being less refracted 
than the lower, they often appear to be oval when near 
the horizon. The looming also or elevation of coasts, 
mountains, and ships, when viewed across the sea, 
arises from unusual refraction. A friend of the au- 
thor, while standing on the plains of Hindostan, saw 
the whole upper chain of the Himalaya mountains start 
into view, from a sudden change in the density of the 
air, occasioned by a heavy shower after a very long 
course of dry and hot weather. Single and double im- 
ages of objects at sea, arising from sudden changes of 



Scr. XVm. PHENOMENA FROM REFLECTION. 151 

temperature which are not so soon communicated to the 
water on account of its density as to the air, occur more 
rarely and are of shorter duration than similar appear- 
ances on land. In 1818, Captain Scoresby, whose ob- 
servations on the phenomena of the polar seas are so 
valuable, recognized his father's ship by its inverted 
image in -the air, although the vessel itself was below 
the horizon. He afterward found that she was seven- 
teen miles beyond the horizon, and thirty miles distant. 
Two images are sometimes seen suspended in the air 
over a ship, one direct and the other inverted, with their 
topmasts or their hulls meeting, according as the in- 
verted image is above or below the direct image (N. 188^. 
Dr. Wollaston has proved that these appearances are 
owing to the refraction of the rays through media of 
different densities, by the veiy simple experiment of 
looking along a red-hot poker at a distant object. Two 
images are seen, one direct and another inverted, in 
consequence of the change induced by the heat in the 
density of the adjacent air. He produced the same 
effect by a saline or saccharine solution with water and 
spirit of wine floating upon it (N. 189). 

Many of the phenomena that have been ascribed to 
extraordinary refraction seem to be occasioned J>y a 
partial or total reflection of the rays of light at the sur- 
faces of strata of different densities (N. 184). It is well 
known that when light falls obliquely uponjhe external 
surface of a transparent medium, as on a plate i glass 
or stratum of air, one portion is reflected and the other 
transmitted. But when light falls very obliquely upon 
the internal surface, the whole is reflected and not a 
ray is transmitted. In all cases the an^es made by 
the incident and reflected rays with a perpendicular to 
the surface being equal, as the brightness of the re- 
flected image depends on the quantity of light, those 
arising from total reflection must be by far the most 
vivid. The delusive appearance of water, so well 
known to African travelers and to the Arab of the des- 
ert as the Lake of the Gazelles, is ascribed to the re- 
flection which takes place between strata of air of dif- 
ferent densities, owing to radiation of heat from the 
arid sandy plains. The 'mirage described by Captain 



152 EXTRAORDINARY REFLECTION. SECT. XVIII. 

Mundy in his Journal of a Tour in India probably 
arises from this cause. A deep precipitous valley be- 
low us, at the bottom of which I had seen one or two 
miserable villages in the morning, bore in the evening a 
complete resemblance to a beautiful lake ; the vapor 
which played the part of water ascending nearly half 
way up the sides of the vale, and on its bright surface 
trees and rocks being distinctly reflected. I had not 
been long contemplating this phenomenon, before a 
sudden storm came on and dropped a curtain of clouds 
over the scene." 

An occurrence which happened on the 18th of No- 
vember, 1804, was probably produced by reflection. 
Dr. Buchan, while watching the rising sun from the 
cliff about a mile to the east of Brighton, at the instant 
the solar disc emerged from the surface of the ocean, 
saw the cliff on which he was standing, a windmill, his 
own figure and that of a friend, depicted immediately 
opposite to him on the sea. This appearance lasted 
about ten minutes, till the sun had risen nearly his own 
diameter above the surface of the waves. The whole 
then seemed to be elevated into the air and successively 
vanished. The rays of the sun fell upon the cliff at an 
incidence of 73 from the perpendicular, and the sea 
was covered with a dense fog many yards in height 
which gradually receded before the rising sun. When 
extraordinary refraction takes place laterally, the strata 
of variable density are perpendicular to the horizon, 
and if combined with vertical refraction, the objects 
are magnified as when seen through a telescope. From 
this cause,, on 'the 2(>'th of July, 1798, the cliffs of 
France, fifty' "miles oi'f, were seen as distinctly from 
Hastings as if they had been close at hand ; and even 
Dieppe was said to have been visible in the afternoon. 

The stratum of air in the horizon is so much thicker 
and more dense than the stratum in the vertical, that 
the sun's light is diminished 1300 times in passing 
through it, which enables us to look at him when setting 
without being dazzled. The loss of light and conse- 
quently of heat by the absorbing power of the atmos- 
phere, increases with the obliquity of incidence. Of 
ten thousand rays falling on its surface, 8123 arrive at a 



SECT. XIX. ATMOSPHERIC ABSORPTION. 153 

given point of the earth if they fall perpendicularly ; 
7024 arrive, if the angle of direction be fifty degrees ; 
2831, if it be seven degrees ; and only five rays will 
arrive through a horizontal stratum. Since so great a 
quantity of light is lost in passing through the atmos- 
phere, many celestial objects may be altogether invisible 
from the plain, which may be seen from elevated situ- 
ations. Diminished splendor, and the false estimate 
we make of distance from the number of intervening 
objects, lead us to suppose the sun and moon to be 
much larger when in the horizon than at any other al- 
titude, though their apparent diameters are then some- 
what less. Instead of the sudden transitions of light 
and darkness, the reflective power of the air adorns na- 
ture with the rosy and golden hues of the Aurora and 
twilight. Even when the sun is eighteen degrees be- 
low the horizon, a sufficient portion of light remains to 
show, that at the height of thirty miles it is still dense 
enough to reflect light. The atmosphere scatters the 
sun's rays, and gives all the beautiful tints and cheerful- 
ness of day. It transmits the blue light in greatest 
abundance ; the higher we ascend, the sky assumes a 
deeper hue ; but in the expanse of space, the sun and 
stars must appear like brilliant specks in profound 
blackness. 




SECTION XIX. 

Constitution of Light according to Sir Isaac Ne^ 
Colors of Bodies Constitution of Light accord 
ster New Colors in the Solar Spectrum Frau 
Dispersion of Light The Achromatic Telescope 
Accidental and Complementary Colors M. Plateau's 
Theory of Accidental Colors. 

IT is impossible thus to trace the path of a sunbeam 
through our atmosphere without feeling a desire to 
know its nature, by what power it traverses the immen- 
sity of space, and the various modifications it undergoes 
at the surfaces and in the interior of terrestrial sub- 
stances. 

Sir Isaac Newton proved the compound nature of 
white light as emitted from the sun, by passing a sun- 
beam through a glass prism (N. 190), which separating 



154 CONSTITUTION OF LIGHT. SECT. XIX. 

the rays by refraction, formed a spectrum or oblong 
image of the sun, consisting of seven colors, red, orange, 
yellow, green, blue, indigo, and violet ; of which the 
red is the least refrangible and the violet the most. But 
when he reunited these seven rays by means of a lens, 
the compound beam became pure white as before. He 
insulated each colored ray ; and finding that it was no 
longer capable of decomposition by refraction, concluded 
that white light consists of seven kinds of homogeneous 
light, and that to the same color the same refrangibility 
ever belongs, and to the same refrangibility the same 
color. Since the discoveiy of absorbent media, how- 
ever, it appears that this is not the constitution of the 
solar spectrum. 

We know of no substance that is either perfectly 
opaque or perfectly transparent. Even gold may be 
beaten so thin as to be pervious to light. On the con- 
trary, the clearest crystal, the purest air or water, stops 
or absorbs its rays when transmitted, and gradually ex- 
tinguishes them as they penetrate to greater depths. 
On this account objects cannot be seen at the bottom of 
very deep water, and many more stars are visible to the 
naked eye from the tops of mountains than from the 
valleys. The quantity of light that is incident on any 
transparent substance is always greater than the sum of 
the reflected and refracted rays. A small quantity is 
irregularhy-efleeted in all directions by the imperfec- 
tions of the polish by which we are enabled to see the 
surface ; but a much greater portion is absorbed by the 
body. Bodies that reflect all the rays appear white, 
those that absorb them all seem black ; but most sub- 
stances, after decomposing the white light which falls 
upon them, reflect some colors and absorb the rest. A 
violet reflects the violet rays alone, and absorbs the 
others. Scarlet cloth absorbs almost all the colors ex- 
cept red. Yellow cloth reflects the yellow rays most 
abundantly, and blue cloth those that are blue. Con- 
sequently color is not a property of matter, but arises 
from the action of matter upon light. Thus a white 
riband reflects all the rays, but when dyed red the par- 
ticles of the silk acquire the property of reflecting the 
red rays most abundantly and of absorbing the others. 



S*CT. XIX. ABSORPTION OF LIGHT. 155 

Upon this property of unequal absorption, the colors of 
transparent media depend. For they also receive their 
color from their power of stopping or absorbing some of 
the colors of white light and transmitting others. As 
for example, black and red inks, though equally homo- 
geneous, absorb different kinds of rays ; and when ex- 
posed to the sun, they become heated in different de- 
grees ; while pure water seems to transmit all rays 
equally, and is not sensibly heated by the passing light 
of the sun. The rich dark light transmitted by a smalt- 
blue finger-glass is not a homogeneous color like the 
blue or indigo of the spectrum, but is a mixture of all 
the colors of white light which the glass has not ab- 
sorbed. The colors absorbed are such as mixed with 
the blue tint would form white light. When the spec- 
trum of seven colors is viewed through a thin plate of 
this glass they are all visible ; and when the plate is 
very thick, every color is absorbed between the extreme 
red and the extreme violet, the interval being perfectly 
black : but if the spectrum be viewed through a certain 
thickness of the glass intermediate between the two, it 
will be found that the middle of the red space, the whole 
of the orange, a great part of the green, a considerable 
part of the blue, a little of the indigo, and a very little 
of the violet, vanish, being absorbed by the blue glass : 
and that the yellow rays -occupy a larger space, cover- 
ing part of that formerly occupied by the orange on one 
side, and by the green on the other. So that the blue 
glass absorbs the red light, which when mixed with the 
yellow constitutes orange ; and also absorbs the blue 
light, which when mixed with the yellow forms the 
part of the green space next to the yellow. Hence by 
absorption, green light is decomposed into yellow and 
blue, and orange light into yellow and red. Conse- 
quently the orange and green rays, though incapable of 
decomposition by refraction, can be resolved by absorp- 
tion, and actually consist of two different colors possess- 
ing the same' degree of refrangibility. Difference of 
color, therefore, is not a test of difference of refrangi- 
bility, and the conclusion deduced by Newton is no 
longer admissible as a general truth. By this analysis 
of the spectrum, not only with blue glass, but with a 



156 THE SOLAR SPECTRUM. SECT. XIX. 

variety of colored media, Sir David Brewster, so justly 
celebrated for his optical discoveries, has proved that 
the solar spectrum consists of three primary colors, red, 
yellow, and blue, each of which exists throughout its 
whole extent, but with different degrees of intensity in 
different parts ; and that the superposition of these three 
produces all the seven hues according as each primary 
color is an excess or defect. Since a certain portion of 
red, yellow, and blue rays constitute white light, the 
color of any point of the spectrum may be considered 
as consisting of the predominating color at that point 
mixed with white light. Consequently, by absorbing 
the excess of any color at any point of the spectrum 
above what is necessary to form white light, such white 
light will appear at that point as never mortal eye 
looked upon before this experiment, since it possesses 
the remarkable property of remaining the same after 
any number of refractions, and of being capable of de- 
composition by absorption alone. 

In addition to the seven colors of the Newtonian spec- 
trum, Sir John Herschel has discovered a set of very 
dark red rays beyond the red extremity of the spec- 
trum, which can only be seen when the eye is defended 
from the glare of the other colors by a dark blue cobalt 
glass. He has also found that beyond the extreme 
violet there are visible rays of a lavender gray color, 
which may be seen by throwing the spectrum on a 
sheet of paper moistened by the carbonate of soda. 
The illuminating power of the different rays of the spec- 
trum varies with the color. The most intense light is 
in the mean yellow ray. 

When the prism is very perfect and the sunbeam 
small, so that the spectrum may be received on a sheet 
of white paper in its utmost state of purity, it presents 
the appearance of a riband shaded with all the prismatic 
colors, having its breadth irregularly striped or subdi- 
vided by an indefinite number of dark, and sometimes 
black, lines. The greater number of these rayless lines 
are so extremely narrow that it is impossible to see 
them in ordinary circumstances. The best method is 
to receive the spectrum on the object glass of a tele- 
scope, so as to magnify them sufficiently to render them 



SECT. XIX. FRAUNHOFER'S LINES. 157 

visible. This experiment may also be made, but in an 
imperfect manner, by viewing a narrow slit between two 
nearly closed window-shutters through a very excellent 
glass prism held close to the eye, with its refracting 
angle parallel to the line of light. The rayless lines in 
the red portion of the spectrum become most visible as 
the sun approaches the horizon, while those in the blu 
extremity are most obvious in the middle of the day. 
AVhen the spectrum is formed by the sun's rays, either 
direct or indirect as from the sky, clouds, rainbow, moon, 
or planets the black bands are always found to be in 
the same parts of the spectrum, and under all circum- 
stances to maintain the same relative positions, breadths, 
and intensities. Similar dark lines are also seen in the 
light of the stars, in the electric light, and, in the flame 
of combustible substances, though differently arranged, 
each star and each flame having a system of dark lines 
peculiar to itself, which remains the same under every 
circumstance. Dr. Wollaston and M. Fraunhofer of 
Munich discovered these lines deficient of rays inde- 
pendently of each other. M. Fraunhofer found that 
their number extends to nearly six hundred. There are 
bright lines in the solar spectrum which also maintain a 
fixed position. Among the dark lines, M. Fraunhofer 
selected seven of the most remarkable, and determined 
their distances so accurately, that they now form stand- 
ard and invariable points of reference for measuring the 
refractive powers of different media on the rays of light, 
which renders this department of optics as exact as any 
of the physical sciences. These lines are designated 
by the letters of the alphabet, beginning with B, which 
is in the red near the end of the spectrum ; c is farther 
advanced in the red ; D is in the orange ; E, in the 
green ; F, in the blue; G, in the indigo; and H, in the 
violet. By means of these fixed points, M. Fraunhofer 
has ascertained from prismatic observation the refrangi- 
bility of seven of the principal rays in each often differ- 
ent substances solid and liquid. The refraction increased 
in all from the red ta the violet end of the spectrum ; 
but so irregularly for each ray and in each medium, that 
no law (ioukl be discovered. The rays that are wanting 
in the solar spectrum which occasion the dark lines, 
O 



158 DISPERSION OF LIGHT. SECT. XIX. 

were supposed to be absorbed by the atmosphere of the 
sun. If they were absorbed by the earth's atmosphere, 
the very same rays would be wanting in the spectra 
from the light of the fixed stars, which is not the case ; 
for it has already been stated that the position of the 
dark lines is not the same in spectra from starlight and 
from the light of the sun. The solar rays reflected 
from the moon and .planets would most likely be mod- 
ified also by their atmospheres, but they are not : for 
the dark lines have precisely the same positions in the 
spectra, from the direct and reflected light of the sun. 
But the annular eclipse which happened on the 15th of 
May, 1836, afforded Professor Forbes the means of 
proving that the dark lines in question cannot be attrib- 
uted to the absorption of the solar atmosphere ; they 
were neither broader nor more numerous in the spec- 
trum formed during that phenomenon than at any other 
time, though the rays came only from the circumference 
of the sun's disc, and consequently had to traverse a 
greater depth of his atmosphere. We are therefore 
still ignorant of the cause of these rayless bands. 

A sunbeam received on a screen, after passing through 
a small round hole in a window-shutter, appears like a 
round white spot ; but when a prism is interposed, the 
beam no longer occupies the same space. It is separa- 
ted into, the prismatic colors, and spread over a line of 
considerable length, while its breadth remains the same 
with that of the white spot. The act of spreading or 
separation is called the dispersion of the colored rays. 
Dispersion always takes place in the plane of refraction, 
and is greater as the angle of incidence is greater. It 
varies inversely as the length of a wave of light, and 
directly as its velocity : hence toward the blue end of 
the spectrum, where the undulations of the rays are 
least, the dispersion is greatest. Substances have veiy 
different dispersive powers ; that is to say the spectra 
formed by two equal prisms of different substances under 
precisely the same circumstances, are of different 
lengths. Thus, if a prism of flint glass and one of crown 
glass of equal refracting angles be presented to two rays 
of white light at equal angles, it will be found, that the 
space over which the colored rays are dispersed by the 



SJCT. XIX. THE ACHROMATIC TELESCOPE. 159 

flint glass is much greater than the space occupied by 
that produced by the crown glass ; and as the quantity 
of dispersion depends upon the refracting angle of the 
prism, the angles of the two prisms may be made such, 
that when the prisms are placed close together with tbjeir 
edges turned opposite ways, they will exactly oppose 
each other's action, and will refract the colored rays 
equally but in contrary directions, so that an exact com- 
pensation will be effected, and the light will be refracted 
without color (N. 191). The achromatic telescope is 
constructed on this principle. It consists of a tube with 
an object glass or lens at one end to bring the rays to a 
focus and form an image of the distant object, and a 
magnifying glass at the other end to view the knage 
thus formed. Now it is found that the object-glass, 
instead of making the rays converge to one point, dis- 
perses them, and gives a confused and colored image : 
but by constructing it of two lenses in contact, one of 
flint and the other of crown glass of certain forms and 
proportions, the dispersion is counteracted, and a per- 
fectly well defined and colorless image of the object is 
formed (N. 192). It was thought to be impossible to 
produce refraction without color, till Mr. Hall, a gentle- 
man of "Worcestershire, constructed a telescope on this 
principle in the year 1733 ; and twenty-five years after- 
ward, the achromatic telescope was brought to perfec- 
tion by Mr. Dollond, a celebrated optician in London. 

A perfectly homogeneous color is very rarely to be 
found, but the tints of all substances are most brilliant 
when viewed in light of their own color. The red of a 
wafer is much more vivid in red than in white light ; 
whereas if placed in homogeneous yellow light, it can 
no longer appear red, because there is not a ray of red 
in the yellow light. Were it not that the wafer, like all 
other bodies, whether colored or not, reflects white light 
at its outer surface, it would appear absolutely black 
when placed in yellow light. 

After looking steadily for a short time at a colored 
object, such as a red wafer, on turning the eyes to a 
white substance, a green image of the wafer appears, 
which is called the accidental color of red. All tints 
have their accidental colors : thus the accidental color 



160 ACCIDENTAL COLORS. SECT. XIX. 

of orange is blue ; that of yellow is indigo ; of green, 
reddish-white ; of blue, orange-red ; of violet, yellow ; 
and of white, black ; and vice versa. When the direct 
and accidental colors are of the same intensity, the acci- 
dental is then called the complementary color, because 
any two colors are said to be complementary to one an- 
other which produce white when combined. 

From recent experiments by M. Plateau of Brussels, 
it appears that two complementary colors from direct 
impression, which would produce white when combined, 
produce black, or extinguish one another by their union, 
when accidental ; and also that the combination of all the 
tints of the solar spectrum produces white light if they 
be from a direct impression on the eye, whereas black- 
ness results from a union of the same tints if they be 
accidental ; and in every case where the real colors pro- 
duce white by their combination, the accidental colors 
of the same tints produce black. When the image of 
an object is impressed on the retina only for a few mo- 
ments, the picture left is exactly of the same color with 
the object, but in an extremely short time the picture 
is succeeded by the accidental image. M. Plateau at- 
tributes this phenomenon to a reaction of the retina after 
being excited by direct vision, so that the accidental im- 
pression is of an opposite nature to the corresponding 
direct impression. He conceives, that when the eye is 
excited by being fixed for a time on a colored object, and 
then withdrawn from the excitement, that it endeavors 
to return to its state of repose, but in so doing that it 
passes this point and spontaneously assumes an opposite 
condition, like a spring, which, bent in one direction, in 
returning to its state of rest bends as much the contrary 
way. The accidental image thus results from a partic- 
ular modification of the organ of sight, in virtue of which 
it spontaneously gives us a new sensation after it has 
been excited by direct vision. If the prevailing impres- 
sion be a very strong white light, its accidental image is 
not black, but, a variety of colors in succession. Accord- 
ing to M. Plateau, the retina offers a resistance to the 
action of light, which increases with the duration of this 
action ; whence, after looking intently at an object for a 
long time, it appears to decrease in brilliancy. The im- 



SECT. XX. INTERFERENCE OF LIGHT 161 

agination has a powerful influence on our optical impres- 
sions, and has been known to revive the images of highly 
luminous objects months, and even years, afterward. 



SECTION XX. 



Interference of Light Undulatory Theory of Light Propagation of Light 
ings M 
equency 
ton's Scale of Colors Diffraction of Light Sir John Herschel's Theory 



gt ropagaon of ight 

Newton'* Rings Measurement of the Length of the Waves of Light, 

Ether for each Color New- 



and of the Frequency of the Vibrations of 
ton's Scale of Colors Diffraction of Light 
of the Absorption of Light Refraction and Reflection of Light. 

NEWTON and most of his immediate successors imag- 
ined light to be a material substance, emitted by all self- 
luminous bodies in extremely minute particles, moving 
in straight lines with prodigious velocity, which, by im- 
pinging upon the optic nerves, produce the sensation of 
light. Many of the observed phenomena have been ex- 
plained by this theory ; it is, howev,er, totally inadequate 
to account for the following circumstances. 

When two equal rays of red light, proceeding from 
two luminous points, fall upon a sheet of "white paper in 
a dark room, they produce a red spot on it, which will 
be twice as bright as either ray would produce singly, 
provided the difference in the lengths of the two'beams, 
from the luminous points to the red spot on the paper, 
bo exactly the 0-0000258th part of an inch. The same 
effect wiU take place if the difference in the lengths be 
twice, three times, four times, &c. that quantity. But 
if the difference in the lengths of the two rays be equal 
to one-half of the 0-0000258th part of an inch, or to its 
H, 2|, 3|, &c. part, the one light will entirely extinguish 
the other, and will produce absolute darkness on the 
paper where the united beams fall. If the difference 
in the lengths of their paths be equal to the 1|, 2|, 3|, 
&c. of the 0-0000258th part of an inch, the red spot 
arising from the combined beams will be of the same 
intensity which one alone would produce. If violet light 
be employed, the difference in the lengths of the two 
beams must be equal to the 0'0000157th part of'an inch 
in order to produce the same phenomena ; and for the 
other colors, the difference must be intermediate be^ 



162 INTERFERENCE OF LIGHT. SECT. XX- 

tween the 0-0000258th and the 0-0000157th part of an 
inch. Similar phenomena may be seen by viewing the 
flame of a candle through two very fine slits in a card 
extremely near to one another (N. 193) ; or by admitting 
the sun's light into a dark room through a pin-hole about 
the fortieth of an inch in diameter, receiving the image 
on a sheet of white paper, and holding a slender wire in 
the light. Its shadow will be found to consist of a bright 
white bar or stripe in the middle, with a series of alter- 
nate black and brightly colored stripes on each side. The 
rays which bend round the wire in two streams are of 
equal lengths in the middle stripe; it is consequently 
doubly bright from their combined effect ; but the rays 
which fall on the paper on each side of the bright stripe, 
being of such unequal lengths as to destroy one another, 
form black lines. On each side of these black lines the 
rays are again of such lengths as to combine to form bright 
stripes, and so on alternately till the light is too faint to be 
visible. When any homogeneous light is used, such as 
red, the alternations are only black and red ; but on ac- 
count of the heterogeneous nature of white light, the 
black lines alternate with vivid stripes or fringes of pris- 
matic colors, arising from the superposition of systems 
of alternate black lines and lines of each homogeneous 
color. That the alternation of black lines and colored 
fringes actually does arise from the mixture of the two 
streams of light which flow round the wire, is proved by 
their vanishing the instant one of the streams is inter- 
rupted. It may therefore be concluded, as often as 
these stripes of light and darkness occur, that they are 
owing to the rays combining at certain intervals to pro- 
duce a joint effect, and at others to extinguish one 
another. Now it is contrary to all our ideas of matter 
to suppose that two particles of it should annihilate one 
another under any circumstances whatever ; while on 
the contrary, two opposing motions may, and it is im- 
possible not to be struck with the perfect similarity be- 
tween the interferences of small undulations of air or of 
water and the preceding phenomena. The analogy is 
indeed so perfect, that philosophers of the highest au- 
thority concur in the supposition that the celestial regions 
are filled with an extremely rare, imponderable, and 



SCT. XX. THE ETHEREAL MEDIUM. 163 

highly elastic medium or ether, whose particles are ca- 
pable of receiving the vibrations communicated to them 
by self-luminous bodies, and of transmitting them to the 
optic nerves, so as to produce the sensation of light. 
The acceleration in the mean motion of Encke's comet, 
as well as of the comet discovered by M. Biela, renders 
the existence of such a medium almost certain. It is 
clear that in this hypothesis, the alternate stripes of 
light and darkness are entirely the effect of the interfe- 
rence of the undulations ; for by actual measurement, 
the length of a wave of the mean red rays of the solar 
spectrum is equal to the 0-0000258th part of an inch ; 
consequently, when the elevation of the waves combine, 
they produce double the intensity of light that each 
would do singly ; and when half a wave combines with 
a whole, that is, when the hollow of one wave is filled 
up by the elevation of another, darkness is the result. 
At intermediate points betwsen these extremes, the in- 
tensity of the light corresponds to intermediate differ- 
ences in the lengths of the rays. 

The theory of interferences is a particular case of the 
general mechanical law of the superposition of small 
motions ; whence it appears that the disturbance of a 
particle of an elastic medium, produced by two coexis- 
tent undulations, is the sum of the disturbances which 
each undulation would produce separately; conse- 
quently, the particle will move in the diagonal of a par- 
allelogram, whose sides are the two undulations. If, 
therefore, the two undulations agree hi direction, or 
nearly so, the resulting motion will be very nearly equal 
to their sum, and in the same direction : if they nearly 
oppose one another, the resulting motion will be nearly 
equal to their difference ; and if the undulations be equal 
and opposite, the resultant will be zero, and the particle 
will remain at rest. 

The preceding experiments, and the inferences de- 
duced from them, which have led to the establishment 
of the doctrine of the undulations of light, are the most 
splendid memorials of our illustrious countryman Dr. 
Thomas Young, though Buy gens was the first to origi- 
nate the idea. 

It is supposed that the particles of luminous bodies 



164 PROPAGATION OF LIGHT. SECT. XX. 

are in a state of perpetual agitation, and that they pos- 
sess the property of exciting regular vibrations in the 
ethereal medium, corresponding to the vibrations of their 
own molecules ; and that, on account of its elastic nature, 
one particle of the ether when set in motion communi- 
cates its vibrations to those adjacent, which in succession 
transmit them to those farther off ; so that the primi- 
tive impulse is transferred from particle to particle y and 
the undulating motion darts through ether like a wave 
in water. Although the progressive motion of light is 
known by experience to be uniform and in a straight 
line, the vibrations of the particles are always at right 
angles to the direction of the ray. The propagation of 
light is like the spreading of waves in water ; but if one 
ray alone be considered, its motion may be conceived by 
supposing a rope of indefinite length stretched horizon- 
tally, one end of which is held in the hand. If it be 
agitated to and fro at regular intervals, with a motion 
perpendicular to its length, a series of similar and equal 
tremors or wavps will be propagated along it ; and if the 
regular impulses be given in a variety of planes, as up 
and down, from right to left, and also in oblique direc- 
tions, the successive undulations will take place in every 
possible plane. An analogous motion in the ether, 
when communicated to the optic nerves, would produce 
the sensation of common light. It is evident that the 
waves which flow from end to end of the cord in a ser- 
pentine form, are altogether different from the perpen- 
dicular vibratory motion of each particle of the rope, 
which never deviates far from a state of rest. So in 
ether, each particle vibrates perpendicularly to the di- 
rection of the ray ; but these vibrations are totally dif- 
ferent from, and independent of, the undulations which 
are transmitted through it, in the same manner as the 
vibrations of each particular ear of corn are independent 
of the waves that rush from end to end of a harvest field 
when agitated by the wind. 

The intensity of light depends upon the amplitude or 
extent of the vibrations of the particles of ether ; while 
its color depends upon their frequency. The time of 
the vibration of a particle of ether is by theory, as the 
length of a wave directly, and inversely as its velocity. 



SECT. xx. NEWTON'S RINGS: 165 

Now, as the velocity of light is known to be 190,000 
miles in a second, if the length of the waves of the dif- 
ferent colored rays could be measured, the number of 
vibrations in a second corresponding to each could be 
computed ; that has been accomplished as follows : 
All transparent substances of a certain thickness, with 
parallel surfaces, reflect and transmit white light ; but 
if they be extremely thin, both the reflected and trans- 
mitted light is colored. The vivid hues on soap-bubbles, 
the iridescent colors produced by heat on polished steel 
and copper, the fringes of color betweefa the laminae of 
Iceland spar and sulphate of lime, all consist of a suc- 
cession of hues disposed in the same order, totally inde- 
pendent of the color of the substance, and determined 
solely by its greater or less thickness, a circumstance 
which affords the means of ascertaining the length of 
the waves of each colored ray, and the frequency of the 
vibrations of the particles producing them. If a plate of 
glass be laid upon a lens of almost imperceptible curva- 
ture, before an open window; when they are pressed to- 
gether a black spot will be seen in the point of contact, 
surrounded by seven rings of vivid colors, all differing 
from one another (N. 194). In the first ring, estimated 
from the black spot, the colors succeed each other in the 
following order : black, very faint blue, brilliant white, 
yellow, orange, and red. They are quite different in 
the other rings, and in the seventh the only colors are 
pale bluish-green and very pale pink. That these rings 
are formed between the two surfaces in apparent con- 
tact may be proved by laying a prism on the lens, in- 
stead of the plate of glass, and viewing the rings through 
the inclined side of it that is next to the eye, which ar- 
rangement prevents the light reflected from the upper 
surface mixing with that from the surfaces in contact, so 
that the intervals between the rings appear perfectly 
black, one of the strongest circumstances in favor of 
the undulatory theory ; for although the phenomena of 
the rings can be explained by either hypothesis, there 
is this material difference, that according to the undu- 
latory theory, the intervals between the rings ought to 
be absolutely black, which is confirmed by experiment ; 
whereas by the doctrine of emanation they ought to be 



1C6 NEWTON'S RINGS. SECT. XX. 

half illuminated, which is not found to be the case. M. 
Fresnel, whose opinion is of the first authority, thought 
this test conclusive. It may therefore be concluded that 
the rings arise entirely from the interference of the 
rays : the light reflected from each of the surfaces in 
apparent contact reaches the eye by paths of different 
lengths, and produces colored and dark rings alternately, 
according as the reflected waves coincide or destroy one 
another. The breadths of the rings are unequal ; they 
decrease in width, and the colors become more crowded, 
as they recede from the center. Colored rings are also 
produced by transmitting light through the same ap- 
paratus ; but the colors are less vivid, and are comple- 
mentary to those reflected, consequently the central spot 
is white. 

The size of the rings increases with the obliquity of 
the incident light ; the same color requiring a greater 
thickness or space between the glasses to produce it than 
when the light falls perpendicularly upon them. Now 
if the apparatus be placed in homogeneous instead of 
white light, the rings will all be of the same color with 
that of the light employed. That is to say, if the light 
be red, the rings will be red divided by black intervals. 
The size of the rings varies with the color of the light. 
They are largest in red, and decrease in magnitude with 
the succeeding prismatic colors, being smallest in violet 
light. 

Since one of the glasses is plane and the other spheri- 
cal, it is evident that from the point of contact, the space 
between them gradually increases in thickness all round, 
so that a certain thickness of air corresponds to each 
color, which in the undulatory system measures the length 
of the wave producing it (N. 195). By actual measure- 
ment, Sir Isaac Newton found that the squares of the di- 
ameters of the brightest part of each ring are as the odd 
numbers, 1, 3, 5, 7, &c. ; and that the squares of. the diam- 
eters of the darkest parts are as the even numbers, 0, 2, 4, 
6, &c. Consequently the intervals between the glasses 
at these points are in the same proportion. If, then, 
the thickness of the air corresponding to any one color 
could be found, its thickness for all the others would be 
known. Now as Sir Isaac Newton knew the radius of 



SECT. XX. LENGTH OF THE UNDULATIONS. 167 

curvature of the lens, and the actual breadth of the 
rings in parts of an inch, it was easy to compute that 
the thickness of air at the darkest part of the first ring 
is the 80 oa part of an inch, whence all the others have 
been deduced. As these intervals determine the length 
of the waves on the undulatory hypothesis, it appears 
that the length of a wave of the extreme red of the 
solar spectrum is equal to the 00000266th part of an 
inch ; that the length of a wave of the extreme violet is 
equal to the 0*00001 67th part of an inch; and as the 
time of a vibration of a particle of ether producing any 
particular color is directly as the length of a wave of that 
color, and inversely as the velocity of light, it follows 
that the molecules of ether producing the extreme red 
of the solar spectrum perform 458 millions of millions 
of vibrations in a second ; and that those producing the 
extreme violet accomplish 727 millions of millions of 
vibrations in the same time. The lengths of the waves 
of the intermediate colors, and the number of then* 
vibrations, being intermediate between these two, white 
light, which consists of all the colors, is consequently 
a mixture of waves of all lengths between the limits of 
the extreme red and violet. The determination of these 
minute portions of time and space, both of which have 
a real existence, being the actual results of measure- 
ment, do as much honor to the genius of Newton as 
that of the law of gravitation. 

The phenomenon of the colored rings takes place in 
vacuo as well as in ah- ; which proves that it is the dis- 
tance between the lenses alone, and not the air, which 
produces the colors. However, if water or oil be put 
between them, the rings contract, but no other change 
ensues ; and Newton found that the thickness of differ- 
ent media at which a given tint is seen, is in the inverse 
ratio of their refractive indices, so that the thickness of 
laminae which could not otherwise be measured, may be 
known by their color ; and as the position of the colors 
in the rings is invariable, they form a fixed standard of 
comparison well known as Newton's scale of colors ; 
each tint being estimated according to the ring to which 
it belongs from the central spot inclusively. Not only 
the periodical colors which have been described, but the 



166- DIFFRACTION OF LIGHT. SECT. XX. 

colors seen in thick plates of transparent substances, the 
variable hues of feathers, of insects' wings, mother of 
pearl, and of striated substances, all depend Upon the same 
principle. To these may be added the colored fringes, 
surrounding the shadows of all bodies held in an ex- 
tremely small beam of light, and the colored rings sur- 
rounding the small beam itself when received on a 
screen. 

When a very slender sunbeam passing through a 
small pin-hole into a dark room is received on a white 
screen, or plate of ground glass, at the distance of a little 
more than six feet, the spot of light on the screen is 
larger than the pin-hole ; and instead of being bounded 
by shadow, it is surrounded by a series of colored rings 
separated by obscure intervals. The rings are more 
distinct in proportion to the smallness of the beam (N. 
196). When the light is white, there are seven rings, 
which dilate or contract with the distance of the screen 
from the hole. As the distance of the screen dimin- 
ishes, the white central spot contracts to a point and 
vanishes ; and on approaching still nearer, the rings 
gradually close in upon it, so that the center assumes 
successively the most intense and vivid hues. When 
the light is homogeneous, red, for example, the rings 
are alternately red and black, and more numerous : and 
their breadth varies with the color, being broadest in red 
light and narrowest in violet. The tints of the colored 
fringes from white light, and their obliteration after the 
seventh ring, arise from the superposition of the differ- 
ent sets of fringes of all the colored rays. The shadows 
of objects are also bordered by colored fringes when 
held in this slender beam of light. If the edge of a 
knife or a hair, for example, be held in it, the rays, in- 
stead of proceeding in straight lines past its edge, are 
bent when quite close to it, and proceed from thence to 
the screen in curved lines called hyperbolas ; so that the 
shadow of the object is enlarged ; and instead of being 
at once bounded by light, is surrounded or edged with 
colored fringes alternating with black bands, which are 
more distinct the smaller the pin-hole (N. 197). The 
fringes are altogether independent of the form or density 
of the object, being the same when it is round or pointed, 



8cr. XX. ABSORPTION OF LIGHT. 169 

when of glass or platina. When the rays which form 
the fringes arrive at the screen, they are of different 
lengths, in consequence of the curved path they follow 
after passing the edge of the object. The waves are 
therefore in different phases or states of vibration, and 
either conspire to form colored fringes or destroy one 
another in the obscure intervals. The colored fringes 
bordering the shadows of objects were first described by 
Grirnaldi in 1665; but besides these he noticed that 
there are others within the shadows of slender bodies 
exposed to a small sunbeam, a phenomenon which has 
already been mentioned to have afforded Dr. Young the 
means of proving beyond all controversy, that colored 
rings are produced by the interference of light. 

It may be concluded, that material substances derive 
their colors from two different causes : some from the 
law of interference, such as iridescent metals, peacocks' 
feathers, &c.; others from the unequal absorption of 
the rays of white light, such as vermilion, ultramarine, 
blue, or green cloth, flowers, and the greater number of 
colored bodies. The latter phenomena have been con- 
sidered extremely difficult to reconcile with the undula- 
tory theory of light, and much discussion has arisen as 
to what becomes of the absorbed rays. But that em- 
barrassing question has been ably answered by Sir John 
Herschel in a most profound paper, On the Absorption 
of Light by colored Media, and cannot be better given 
than in his own words. It must however be premised, 
that as all transparent bodies are traversed by light, 
they are presumed to be permeable to the ether. He 
says, " Now, as regards only the general feet of the ob- 
struction and ultimate extinction of light in its passage 
through gross media, if we compare the corpuscular and 
undulatory theories, we shall find that the former ap- 
peals to our ignorance, the latter to our knowledge, for 
its explanation of the absorptive phenomena. In at- 
tempting to explain the extinction of light on the corpus- 
cular doctrine, we have to account for the light so extin- 
guished as a material body, which we must not suppose 
annihilated. It may however be transformed; and 
among the imponderable agents, heat, electricity, &c., 
it may be that we are to search for the light which has 



170 ABSORPTION 01' LIGHT SECT. XX. 

become thus comparatively stagnant. The heating 
power of the solar rays gives a primd facie plausibility 
to the idea of the transformation of light into heat by 
absorption. But when we come to examine the matter 
more nearly, we find it encumbered on all sides with 
difficulties. How is it, for instance, that the most lu- 
minous rays are not the most calorific ; but that on the 
contrary, the calorific energy accompanies, in its great- 
est intensity, rays which possess comparatively feeble 
illuminating powers ? These and other questions of a 
similar nature may perhaps admit of answer in a more 
advanced state of our knowledge ; but at present there 
is none obvious. It is not without reason, therefore, 
that the question ' What becomes of light ?' which ap- 
pears to have been agitated among the photologists of 
the last century, has been regarded as one of consider- 
able importance as well as obscurity by the corpuscular 
philosophers. On the other hand, the answer to this 
question, afforded by the undulatory theory of light, is 
simple and distinct. The question, ' What becomes of 
light ?' merges in the more general one, ' What becomes 
of motion ? ' And the answer, on dynamical principles, 
is, that it continues forever. No motion is, strictly 
speaking, annihilated ; but it may be divided, and the 
divided parts made to oppose and, in effect, destroy one 
another. A body struck, however perfectly elastic, 
vibrates for a time, and then appears to sink into its 
original repose. But this apparent rest (even abstract- 
ing from the inquiry that part of the motion which may 
be conveyed away by the ambient air) is nothing else 
than a state of subdivided and mutually destroying mo- 
tion, in which every molecule continues to be agitated 
by an indefinite multitude of internally reflected waves, 
propagated through it in every possible direction, from 
eveiy point in its surface on which they successively 
impinge. The superposition of such waves will, it is 
easily seen, at length operate their mutual destruction, 
which will be the more complete the more irregular the 
figure of the body, and the greater the number of inter- 
nal reflections." Thus Sir John Herschel, by referring 
the absorption of, light to the subdivision and mutual 
destruction of the vibrations of ether in the interior of 



SCT. XX. TRANSMISSION OP LIGHT 171 

bodies, brings another class of phenomena under the 
laws of the undulatory theory. 

The ethereal medium pervading space is supposed to 
penetrate all material substances, occupying the inter- 
stices between their molecules; but in the interior of 
refracting media it exists in a state of less elasticity 
compared with ks density in vacuo ; and the more 
refractive the medium, the less the elasticity of the 
ether within it. Hence the waves of light are trans- 
mitted with less velocity in such media as glass and 
water than in the' external ether. As soon as a ray of 
light reaches the surface of a diaphanous reflecting sub- 
stance, for example a plate of glass, it communicates its 
undulations to the ether next in contact with the surface, 
which thus becomes a new center of motion, and two 
hemispherical waves are propagated from each point of 
this surface ; one of which proceeds forward into the 
interior of the glass, with E less velocity than the inci- 
dent waves ; and the other is transmitted back into the 
air, with a velocity equal to that with which -it' came 
(N. 198). Thus when refracted, the light moves with 
a different velocity without and within the glass ; when 
reflected, the ray comes and goes with the same ve- 
locity. The particles of ether without the glass, which 
communicate their motions to the particles of the dense 
and less elastic ether within it, are analogous to small 
elastic balls striking large ones ; for some of the motion 
will be communicated to the large balls, and the small 
ones will be reflected. The first would cause the 
refracted wave ; and the last the reflected. Conversely, 
when the light passes from glass to air, the action is 
similar to large balls striking small ones. The small 
balls receive a motion which would cause the refracted 
ray, and the part of the motion retained by the large 
ones would occasion the reflected wave ; so that when 
light passes through a plate of glass or of any other 
medium differing in density from the air, there is a 
reflection at both surfaces ; but this difference exists 
between the two reflections, that one is caused by a 
vibration in the same direction with that of the incident 
ray, and the other by a vibration in the opposite direction. 

A single wave of air or ether would not produce the 



172 ACTION OF LIGHT ON THE RETINA. SECT. XXI. 

sensation of sound or light. In order to excite vision, 
the vibrations of the molecules of ether must be regular, 
periodical, and very often repeated; and as the ear 
continues to be agitated for a short time after the im- 
pulse by which alone a sound becomes continuous, so 
also the fibres of the retina, according to M. d'Arcet, 
continue to vibrate for about the eighth part of a second, 
after the exciting cause has ceased. Every one must 
have observed, when a strong impression is made by a 
bright light, that an object remains visible for a short 
time after shutting the eyes, which is supposed to be 
in consequence of the continued vibrations of the fibres 
of the retina. Occasionally the retina becomes insen- 
sible to feebly illuminated objects when continuously 
presented. If the eye be turned aside for a moment, 
the object becomes again visible. It is probably on this 
account that the owl makes so peculiar a motion with 
its head when looking at objects in the twilight. It is 
quite possible that many vibrations may be excited in 
the ethereal medium incapable of producing undulations 
in the fibres of the human retina, which yet have a 
powerful effect on those of other animals or of insects. 
Such may receive luminous impressions of which wo 
are totally unconscious, and at the same time they may 
be insensible to the light and colors which affect our 
eyes ; their perceptions beginning where ours end. 



SECTION XXL 

Polarization of Light Defined Polarization by Refraction Properties of 
the Tourmaline Double Refraction All doubly Refracted Light is 
Polarized Properties of Iceland Spar Tourmaline absorbs one of the 
two Refracted Rays Undulations of Natural Light Undulations of 
Polarized Light The Optic Axes of Crystals M. Fresnel's Discoveries 
on the Rays passing along the Optic Axis Polarization by Reflection. 

IN giving a sketch of the constitution of light, it is 
impossible to omit the extraordinary property of its po- 
larization, "the phenomena of which," Sir John Her- 
schel says, "are so singular and various, that to one 
who has only studied the common branches of physical 
optics it is liko entering into a new world, so splendid 



SECT. XXI. POLARIZATION BY BEFB ACTION. 173 

as to render it one of the most delightful branches of 
experimental inquiry, and so fertile in the views it lays 
open of the constitution of natural bodies, and the 
minuter mechanism of the universe, as to place it in the 
very first rank of the physico-mathematical sciences, 
which it maintains by the rigorous application of geome- 
trical reasoning its nature admits and requires. 

Light is said to be polarized, which, by being once 
reflected or refracted, is rendered incapable of being 
again reflected or refracted at certain angles. In gene- 
ral, when a ray of light is reflected from a pane of plate- 
glass, or any other substance, it may be reflected a 
second time from another surface, and it will also pass 
freely through transparent bodies. But if a ray of light 
be reflected from a pane of plate-glass at an angle of 
57, it is rendered totally incapable of reflection at the 
surface of another pane of glass in certain definite po- 
sitions, but it will be completely reflected by the second 
pane in other positions. It likewise loses the property 
of penetrating transparent bodies in particular positions, 
while it is freely transmitted by them in others. Light 
so modified as to be incapable of reflection and trans- 
mission in certain directions, is said to be polarized. 
This name was originally adopted from an imaginary 
analogy in the arrangement of the particles of light on 
the corpuscular doctrine to the poles of a magnet, and is 
still retained in the undulatory theory. 

Light may be polarized by reflection from any polished 
surface, and the same property is also imparted by re- 
fraction. It is proposed to explain these methods of 
polarizing light, to give a short account of its most re- 
markable properties, and to endeavor to describe a few 
of the splendid phenomena it exhibits. 

If a brown tourmaline, which is a mineral generaDy 
crystalized in the form of a long prism, be cut longitu- 
dinally, that is, parallel to the axis of the prism, into 
plates about the thirtieth of an inch in thickness, and 
the surfaces polished, luminous objects may be seen 
through them, as through plates of colored glass. The 
axis of each plate is in its longitudinal section parallel to 
the axis of the prism whence it was cut (N. 199). If 
pne of these plates be held perpendicularly between 



174 POLARIZATION BY REFRACTION. SECT. XXI. 

the eye and a candle, and turned slowly round in its 
own plane, no change will take place in the image of 
the candle. But if the plate be held in a fixed position, 
with its axis or longitudinal section vertical, when a 
second plate of tourmaline is interposed between it and 
the eye, parallel to the first, and turned slowly round in 
its own plane, a remarkable change will be found to 
have taken place in the nature of the light. For the 
image of the candle will vanish and appear alternately 
at every quarter revolution of the plate, varying through 
all degrees of brightness down to total, or almost total 
evanescence, and then increasing again by the same de- 
grees as it had before decreased. These changes de- 
pend upon the relative positions of the plates. When 
the longitudinal sections of the two plates are parallel, 
the brightness of the image is at its maximum ; and 
when the axes of the sections cross at right angles, the 
image of the candle vanishes. Thus the light, in pass- 
ing through the first plate of tourmaline, has acquired a 
property totally different from the direct light of the 
candle. The direct light would have penetrated the 
second plate equally well in all directions, whereas the 
refracted ray will only pass through it in particular po- 
sitions, and is altogether incapable of penetrating it in 
others. The refracted ray is polarized in its passage 
through the first tourmaline, and experience shows that 
it never loses that property, unless when acted upon by 
a new substance. Thus, one of the properties of po- 
larized light is the incapability of passing through a plate 
of tourmaline perpendicular to it, in certain positions, 
and its ready transmission in other positions at right 
angles to the former. 

Many other substances have the property of polar- 
izing light. If a ray of light falls upon a transparent 
medium, which has the same temperature, density, and 
structure throughout every part, as fluids, gases, glass, 
&c., and a few regularly crystalized minerals, it is re- 
fracted into a single pencil of light by the laws of ordi- 
nary refraction, according to which the ray, passing 
through the refracting surface from the object to the 
eye, never quits a plane perpendicular to that surface. 
Almost all other bodies, such as the greater number of 



Scr. XXI. DOUBLE REFRACTION. 175 

crystaKzed minerals, animal and vegetable substances, 
gums, resins, jellies, and all solid bodies having unequal 
tensions, whether from unequal temperature or pres- 
sure, possess the property of doubling the image or ap- 
pearance of an object seen through them in certain 
directions. Because a ray of natural light falling upon 
them is refracted into two pencils, which move with dif- 
ferent velocities, and are more or less separated, accord- 
ing to the nature of the body and the direction of the 
incident ray. Whenever a ray of natural light is thus 
divided into two pencils in its passage through a sub- 
stance, both of the transmitted rays are polarized. Ice- 
land spar, a carbonate of lime, which by its natural 
cleavage may be split into the form of a rhombohedron, 
possesses the property of double refraction in an emi- 
nent degree, as may be seen by pasting a piece of paper 
with a large pin-hole in it, on the side of the spar far- 
thest from the eye. The hole will appear double when 
held to the light (N. 200). One of these pencils is re- 
fracted according to the same law as in glass or water, 
never quitting the plane perpendicular to the refracting 
surface, and is therefore called the ordinary ray. But 
the other does quit the plane, being refracted according 
to a different and much more complicated law, and on 
that account is called the extraordinary ray. For the 
same reason one image is called the ordinary, and the 
other the extraordinary image. When the spar is turned 
round in the same plane, the extraordinary image of the 
hole revolves about the ordinary image which remains 
fixed, both being equally bright. But if the spar be kept 
in one position and viewed through a plate of tourma- 
line, it will be found that as the tourmaline revolves, the 
images vary in their relative brightness one increases 
in intensity till it arrives at a maximum, at the same 
time that the other diminishes till it vanishes, and so on 
alternately at each quarter revolution, proving both rays 
to be polarized. For in one position the tourmaline 
transmits the ordinary ray, and reflects the extraordi- 
nary; and after revolving 90, the extraordinary ray is 
transmitted, and the ordinary ray is reflected. Thus 
another property of polarized light is, that it cannot be 
divided into two equal pencils by double refraction, in 



176 DOUBLE REFRACTION. SECT. XXI. 

positions of the doubly refracting bodies in which a ray 
of common light would be so divided. 

Were tourmaline like other doubly refracting bodies, 
each of the transmitted rays would be double ; but that 
mineral when of a certain thickness, after separating the 
light into two polarized pencils, absorbs that which un- 
dergoes ordinary refraction, and consequently shows 
only one image of an object. On this account, tourma- 
line is peculiarly fitted for analyzing polarized light, 
which shows nothing remarkable till viewed through it 
or something equivalent. 

The pencils of light, on leaving a double refracting 
substance* are parallel ; and it is clear from the prece- 
ding experiments, that they are polarized in planes at 
right angles to each other (N. 201). But that will be 
better understood by considering the change produced 
in common light by the action of the polarizing body. It 
has been shown that the undulations of ether, which 
produce the sensation of common light, are performed 
in every possible plane, at right angles to the direction 
in which the ray is moving. But the case is veiy dif- 
ferent after the ray has passed through a doubly refract- 
ing substance, like Iceland spar. The light then pro- 
ceeds in two parallel pencils, whose undulations are still 
indeed transverse to the direction of the rays, but they 
are accomplished in planes at right angles to one an- 
other, analogous to two parallel stretched cords, one of 
which performs its undulations only in a horizontal 
plane, and the other in a vertical or upright plane (N. 
201). Thus the polarizing action of Iceland spar and 
of all doubly refracting substances is, to separate a ray 
of common light, whose waves or undulations are in 
every plane, into two parallel rays, whose waves or un- 
dulations lie in planes at right angles to each other. The 
ray of common light may be assimilated to a round rod, 
whereas the two polarized rays are like two parallel 
long flat rulers, one of which is laid horizontally on its 
broad surface, and the other horizontally on its edge. 
The alternate transmission and obstruction of one of 
these flattened beams by the tourmaline is similar to the 
facility with which a card may be passed between the 
bars of a grating or wires of a cage, if presented edge- 



S*cr. XXI. THE OPTIC AXES OP CRYSTALS. 177 

ways, and the impossibility of its passing in a transverse 
direction. 

Although it generally happens that a ray of light, in 
passing through Iceland spar, is separated into two po- 
larized rays, yet there is one direction along which it is 
refracted in one ray only, and that according to the or- 
dinary law. This direction is called the optic axis 
(N. 202). Many crystals and other substances have 
two optic axes, inclined to each other, along which a 
ray of light is transmitted in one pencil by the law of 
ordinary refraction. The extraordinary ray is some- 
times refracted toward the optic axis, as in quartz, zir- 
con, ice, &c., which are therefore said to be positive 
crystals ; but when it is bent from the optic axis, as in 
Iceland spar, tourmaline, emerald, beryl, &c., the crys- 
tals are negative, which is the most numerous class. 
The ordinary ray moves with uniform velocity within a 
doubly refracting substance, but the velocity of the ex- 
traordinary ray varies with the position of the ray rela- 
tively to the optic axis, being a maximum when its mo- 
tion within the crystal is at right angles to the optic axis, 
and a minimum when parallel to it. Between these ex- 
tremes its velocity varies according to a determinate law. 

It has been inferred from the action of Iceland spar 
on light, that in all doubly refracting substances, one only 
of two rays is turned aside from the plane of ordinary 
refraction, while the other follows the ordinary law ; and 
the great difficulty of observing the phenomena tended 
to confirm that opinion. M. Fresnel, however, proved 
by a most profound mathematical inquiry, a priori, that 
the extraordinary ray must be wanting in glass and other 
uncrystalized substances, and that it must necessarily 
exist in carbonate of lime, quartz, and other bodies hav- 
ing one optic axis, but that in a numerous class of sub- 
stances which possess two optic axes, both rays must 
undergo extraordinary refraction, and consequently that 
both must deviate from their original plane, and these 
results have been perfectly confirmed by subsequent 
experiments. This theory of refraction, which for gen- 
eralization is perhaps only inferior to the law of gravita- 
tion, has enrolled the name of Fresnel among those 
which pass not away, and makes his early loss a subject 

12 

^g 



178 POLARIZATION NY PLATES OF GLASS. SECT, XXI. 

of deep regret to all who take an interest in the higher 
paths of scientific research. 

When a beam of common light is partly reflected at, 
and partly transmitted through, a transparent surface, 
the reflected and refracted pencils contain equal quanti- 
ties of polarized light, and their planes of polarization 
are at right angles to one another : hence a pile of panes 
of glass will give a polarized beam by refraction. For if 
a ray of common light pass through them, part of it 
will be polarized by the first plate, the second plate will 
polarize a part of what passes through it, and the rest 
will do the same in succession, till the whole beam is 
polarized, except what is lost by reflection at the dif- 
ferent surfaces, or by absorption. This beam is polar- 
ized in a plane at right angles to the plane of reflection, 
that is, at right angles to the plane passing through the 
incident and reflected ray (N. 203). 

By far the most convenient way of polarizing light is 
by reflection. A plane of plate-glass laid upon a piece 
of black cloth, on a table at an open window, will appear 
of a uniform brightness from the reflection of the sky 
or clouds. But if it be viewed through a plate of tour- 
maline, having its axis vertical, instead of being illumi- 
nated as before, it will be obscured by a large cloudy 
spot, having its center quite dark, which will readily be 
found by elevating or depressing the eye, and will only 
be visible when the angle of incidence is 57, that is, 
when the line from the eye to the center of the black 
spot makes an angle of 33 with the surface of the re- 
flector (N. 204). When the tourmaline is turned round 
in its own plane, the dark cloud will diminish, and en- 
tirely vanish when the axis of the tourmaline is horizon- 
tal, and then every part of the surface of the glass will 
be equally illuminated. As the tourmaline revolves, the 
cloudy spot will appear and vanish alternately at every 
quarter revolution. Thus, when a ray of light is inci- 
dent on a pane of plate-glass at an angle of 57, the re- 
flected ray is rendered incapable of penetrating a plate 
of tourmaline, whose axis is in the plane of incidence. 
Consequently it has acquired the same character as if 
it had been polarized by transmission through a plate 
of tourmaline, with its axis at right angles to the plane 



S*tT. XXI. POLARIZATION BY REFLECTION. 179 

of reflection. It is found by experience that this polar- 
ized ray is incapable of a second reflection at certain 
angles and in certain positions of the incident plane. 
For if another pane of plate-glass having one surface 
blackened, be so placed as to make an angle of 33 with 
the reflected ray, the image of the first pane will be re- 
flected in its surface, and will be alternately illuminated 
and obscured at every quarter revolution of the black- 
ened pane, according as the plane of reflection is parallel 
or perpendicular to the plane of polarization. Since 
this happens by whatever means the light has been 
polarized, it evinces another general property of polar- 
ized light, which is, that it is incapable of reflection in a 
plane at right angles to the plane of polarization. 

All reflecting surfaces are capable of polarizing light, 
but the angle of incidence at which it is completely 
polarized is different in each substance (N. 205). It 
appears that the angle for plate-glass is 57 ; in crown- 
glass it is 56 55', and no ray will be completely polar- 
ized by water, unless the angle of incidence be 53 11'. 
The angles at which different substances polarize light 
are determined by a very simple and elegant law, dis- 
covered by Sir David Brewster, " That the tangent of 
the polarizing angle for any medium is equal to the sine 
of the angle of incidence divided by the sine of the angle 
of refraction of that medium." Whence also the re- 
fractive power even of an opaque body is known when 
its polarizing angle has been determined. 

Metallic substances, and such as are of high refractive 
powers, like the diamond, polarize imperfectly. 

If a ray polarized by refraction or by reflection from 
any substance not metallic, be viewed through a piece 
of Iceland spar, each image will alternately vanish and 
reappear at every quarter revolution of the spar, whether 
it revolves from right to left, or from left to right ; which 
shows that the properties of the polarized ray are sym- 
metrical on each side of the plane of polarization. 

Although there be only one angle in each substance 
at which light is completely polarized by one reflection, 
yet it may be polarized at any angle of incidence by a 
sufficient number of reflections. For if a ray falls upon 
the upper surface of a pile of plates of glass at an angle 



180 COLORED IMAGES. SfccT. XXII. 

greater or less than a polarizing angle, a part only of 
the reflected ray will be polarized, but a part of what is 
transmitted will be polarized by reflection at the sur- 
face of the second plate, part at the third, and so on till 
the whole is poralized. This is the best apparatus ; but 
one plate of glass having its inferior surface blackened, 
or even a polished table, will answer the purpose. 

''" ' 



SECTION XXII. 

Phenomena exhibited by the passage of Polarized Light through Mica and 
Sulphate of Lime The Colored Images produced by Polarized Light 
passing through Crystals having one and two Optic Axes Circular 
Polarization Elliptical Polarization Discoveries of MM. Biot, Fresnel, 
and Professor Airy Colored Images produced by the Interference of 
Polarized Rays. 

SUCH is the nature of polarized light and of the laws 
it follows. But it is hardly possible to convey an idea of 
the splendor of the phenomena it exhibits under circum- 
stances which an attempt will now be made to describe. 

If light polarized by reflection from a pane of glass be 
viewed through a plate of tourmaline, with its longitudi- 
nal section vertical, an obscure cloud, with its center 
totally dark, will be seen on the glass. Now let a plate 
of mica, uniformly about the thirtieth of an inch in thick- 
ness, be interposed between the tourmaline and the 
glass ; the dark spot will instantly vanish, and instead of 
it, a succession of the most gorgeous colors will appear, 
varying with every inclination of the mica, from the 
richest reds, to the most vivid greens, blues, and purples 
(N. 206). That they may be seen in perfection, the 
mica must revolve at right angles to its own plane. 
When the mica is turned round in a plane perpendicu- 
lar to the polarized ray, it will be found that there are 
two lines in it where the colors entirely vanish. These 
are the optic axes of the mica, which is a doubly refract- 
ing substance, with two optic axes, along which light is 
refracted in one pencil. 

No colors are visible in the mica, whatever its position 
may be with regard to the polarized light, without the 
aid of the tourmaline, which separates the transmitted 
ray into two pencils of colored light complementary to 



SKCT. XXII. COLORED IMAGES. 181 

one another, that is, which taken together would make 
white light. One of these it absorbs, and transmits the 
other; it is therefore called the analyzing plate. The 
truth of this will appear more readily, if a film of sul- 
phate of lime between the twentieth and sixtieth of an 
inch thick be used instead of the mica. When the film 
is of uniform thickness, only one color will be seen when 
it is placed between the analyzing plate and the reflect- 
ing glass ; as, for example, red. But when the tourma- 
line revolves, the red will vanish by degrees till the film 
is colorless ; then it will assume a green hue, which 
will increase and arrive at its maximum when the tour- 
maline has turned through ninety degrees ; after that 
the green will vanish and the red will reappear, alter- 
nating at each quadrant. Thus the tourmaline separ- 
ates the light which has passed through the film into a 
red and a green pencil ; in one position it absorbs the 
green and lets the red pass, and in another it absorbs 
the red and transmits the green. This is proved by 
analyzing the ray with Iceland spar instead of tourmaline ; 
for since the spar does not absorb the light, two images 
of the sulphate of lime will be seen, one red and the 
other green, and these exchange colors every quarter 
revolution of the spar, the red becoming green, and the 
green red^ and where the images overlap, the color is 
white, proving the red and green to be complementary 
to each other. The tint depends on the thickness of 
the film. Films of sulphate of lime, the 0-00124 and 
0-01818 of an inch respectively, give white light in what- 
ever position they may be held, provided they be per- 
pendicular to the polarized ray ; but films of interme- 
diate thickness will give all colors. Consequently, a 
wedge of sulphate of lime, varying in thickness between 
the 0-00124 and the 0-01818 of an inch, will appear to 
be striped with all colors when polarized light is trans- 
mitted through it. A change in the inclination of the 
film, whether of mica or sulphate of lime, is evidently 
equivalent to a variation in thickness. 

When a plate of mica, held as close to the eyes as 
possible at such an inclination as to transmit the polar- 
ized ray along one of its optic axes, is viewed through the 
tourmaline with, its axis vertical, a most splendid appear- 

Q 



182 COLORED IMAGES. SECT. XXII. 

ance is presented. The cloudy spot in the direction of 
the optic axis is seen surrounded by a set of vividly 
colored rings of an oval form, divided into two unequal 
parts by a black curved band passing through the cloudy 
spot about which the rings are formed. The other optic 
axis of the mica exhibits a similar image (N. 207). 

When the two optic axes of a crystal make a small 
angle with one another, as in nitre, the two sets of rings 
touch externally ; and if the plate of nitre be turned round 
in its own plane, the black transverse bands undergo 
a variety of changes, till at last the whole richly colored 
image assumes the form of the figure 8, traversed by a 
black cross (N. 208). Substances with one optic axis 
have but one set of colored circular rings, with a broad 
black cross passing through its center, dividing the rings 
into four equal parts. When the analyzing plate re- 
volves, this figure recurs at eveiy quarter revolution ; 
but in the intermediate positions it assumes the com- 
plementary colors, the black cross becoming white. 

It is in vain to attempt to describe the beautiful phe- 
nomena exhibited by innumerable bodies, which undergo 
periodic changes in form and color when the analyzing 
plate revolves, but not one of them shows a trace of 
color without the aid of tourmaline or something equiv- 
alent to analyze the light, and as it were to call these 
beautiful phantoms into existence. Tourmaline has the 
disadvantage of being itself a colored substance ; but 
that inconvenience may be obviated by employing a re- 
flecting surface as an analyzing plate. When polarized 
light is reflected by a plate of glass at the polarizing 
angle, it will be separated into two colored pencils; and 
when the analyzing plate is turned round in its own 
plane, it will alternately reflect each ray at every quar- 
ter revolution, so that all the phenomena that have been 
described will be seen by reflection on its surface. 

Colored rings are produced by analyzing polarized 
light transmitted through glass melted and suddenly or 
unequally cooled ; also through thin plates of glass 
bent with the hand, jelly indurated or compressed, &c. 
&c. In short, all the phenomena of colored rings may 
be produced, either permanently or transiently, in a 
variety of substances, by heat and cold, rapid cooling, 



SICT. xxn. cmcuLAR POLARIZATION. 183 

compression, dilatation, and induration ; and so little 
apparatus is necessary for performing the experiments, 
that, as Sir John Herschel says, a piece of window- 
glass or a polished table to polarize the light, a sheet of 
clear ice to produce the rings, and a broken fragment 
of plate -glass placed near the eye to analyze the light, 
are alone requisite to produce one of the most splendid 
of optical exhibitions. 

It has been observed, that when a ray of light, 
polarized by reflection from any surface not metallic, is 
analyzed by a doubly refracting substance, it exhibits 
properties wfiich are symmetrical both to the right and 
left of the plane of reflection, and the ray is then said 
to be polarized according to that plane. This symmetry 
is not destroyed when the ray, before being analyzed, 
traverses the optic axis of a crystal having but one 
optic axis, as evidently appears from the circular forms 
of the colored rings already described. Regularly crys- 
talized quartz, however, forms an exception. ID it, 
even though the rays should pass through the optic 
axis itself, where there is no double refraction, the 
primitive symmetry of the ray is destroyed, and the 
plane of primitive polarization deviates either to the 
right or left of the observer, by an angle proportional 
to the thickness of the plate of quartz. This angular 
motion, or true rotation of the plane of polarization, 
which is called circular polarization, is clearly proved by 
the phenomena. The colored rings produced by all 
crystals having but one optic axis are circular, and 
traversed by a black cross concentric with the rings ; so 
that the light entirely vanishes throughout the space 
inclosed by the interior ring, because there is neither 
double refraction nor polarization along the optic axis. 
But in the system of rings produced by a plate of 
quartz, whose surfaces are perpendicular to the axis of 
the crystal, the part within the interior ring, instead of 
being void of light, is occupied by a uniform tint of red, 
green, or blue, according to the thickness of the plate 
(N. 209). Suppose the plate of quartz to be ^ of an 
inch thick, which will give the red tint to th'e space 
within the interior ring; when the analyzing plate is 
turned in its own plane through an angle of 17|, the 



184 CIRCULAR POLARIZATION. SECT. XXII. 

red hue vanishes. If a plate of rock crystal ^ of an 
inch thick be used, the analyzing plate must revolve 
through 35 before the red tint vanishes, and so on ; 
every additional 25th of an inch in thickness requiring 
an additional rotation of 17^ ; whence it is manifest 
that the plane of polarization revolves in the direction 
of a spiral within the rock crystal. It is remarkable 
that in some crystals of quartz, the plane of polarization 
revolves from right to left, and in others from left to 
right, although the crystals themselves differ apparently 
only by a very slight, almost imperceptible variety in 
form. In these phenomena, the rotation to the right is 
accomplished according to the same laws, and with the 
same energy, as that to the left. But if two plates of 
quartz be interposed which possess different affections, 
the second plate undoes, either wholly or partly, the 
rotatory motion which the first had produced, according 
as the plates are of equal or unequal thickness. When 
the plates are of unequal thickness, the deviation is in 
the direction of the strongest, and exactly the same 
with that which a third plate would produce equal in 
thickness to the difference of the two. 

M. Biot has discovered the same properties in a 
variety of liquids. Oil of turpentine, and an essential 
oil of laurel, cause the plane of polarization to turn to 
the left, whereas the syrup of sugar-cane, and a solu- 
tion of natural camphor by alcohol, turn it to the right. 
A compensation is effected by the superposition or 
mixture of two liquids which possess these opposite 
properties, provided no chemical action takes place. A 
remarkable difference was also observed by M. Biot 
between the action of the particles of the same sub- 
stances when in a liquid or solid state. The syrup of 
grapes, for example, turns the plane of polarization to 
the left as long as it remains liquid ; but as soon as it 
acquires the solid form of sugar, it causes the plane of 
polarization to revolve toward the right, a property 
which it retains even when again dissolved. Instances 
occur also in which these circumstances are reversed. 

A ray of light passing through a liquid possessing the 
power of circular polarization is not affected by mixing 
other fluids with the liquid such as water, ether, alco- 



SECT. XXII. CIRCULAR POLARIZATION. 185 

hol, &c which do not possess circular polarization 
themselves, the angle of deviation remaining exactly the 
same as before the mixture. Whence M. Biot infers 
that the action exercised by the liquids in question 
does not depend upon their mass, but that it is a mole- 
cular action exercised by the ultimate particles of mat- 
ter, which depends solely upon the individual constitu- 
tion, and is entirely independent of the positions and 
mutual distances of the particles with regard to each 
other. These important discoveries show, that circular 
polarization surpasses the power of chemical analysis hi 
giving certain and direct evidence of the similarity or 
difference existing in the molecular constitution of bodies, 
as well as of the permanency of that constitution, or of 
the fluctuations to which it may be liable. For example, 
no chemical difference has been discovered between 
syrup from the sugar-cane and syrup from grapes. Yet 
the first causes the plane of polarization to revolve to 
the right, and the other to the left ; therefore some es- 
sential difference must exist in the nature of then- ulti- 
mate molecules. The same difference is to be traced 
between the juices of such plants as give sugar similar 
to that from the cane, and those which give sugar like 
that obtained from grapes. This eminent philosopher 
is now engaged in a series of experiments on the pro- 
gressive changes in the sap of vegetables at different 
distances from their roots, and on the products that are 
formed at the various epochs of vegetation, from their 
action on polarized light. 

It is a fact established by M. Biot, that in circular 
polarization, the laws of rotation followed by the differ- 
ent simple rays of light are dissimilar in different sub- 
stances. Whence he infers that the deviation of the 
simple rays from one another ought not to result from 
a special property of the luminous principle only, but 
that the proper action of the molecules must also concur 
in modifying the deviations of the simple rays differently 
in different substances. 

One of the many brilliant discoveries of M. Fresne 
is the production of circular and elliptical polarization by 
the internal reflection of light from plate glass. He has 
shown that if light polarized by any of the usual methods 



186 ELLIPTICAL POLARIZATION. SECT. XXII. 

be twice reflected within a glass rhomb (N. 1 G6) of a given 
form, the vibrations of the ether that are perpendicular 
to the plane of incidence will be retarded a quarter of a 
vibration, which causes the vibrating particles to describe 
circles, and the succession of such vibrating particles 
throughout the extent of a wave to form altogether a 
circular helix, or curve like a corkscrew. However, 
that only happens when the plane of polarization is 
inclined at an angle of 45 to the plane of incidence. 
When these two planes form an angle either greater 
or less, the succession of vibrating particles forms an 
elliptical helix, which curve may be represented by 
twisting a thread in a spiral about an oval rod. These 
curves will turn to the right or left, according to the 
position of the incident plane. 

The motion of the ethereal medium in elliptical and 
circular polarization may be represented by the analogy 
of a stretched cord ; for if the extremity of such a cord 
be agitated at equal and regular intervals by a vibratory 
motion entirely confined to one plane, the cord will be 
thrown into an undulating curve lying wholly in that 
plane. If to this motion there be superadded another 
similar and equal, but perpendicular to the first, the 
cord will assume the form of an elliptical helix ; its ex- 
tremity will describe an ellipse, and every molecule 
throughout its length will successively do the same. But 
if the second system of vibrations commence exactly a 
quarter of an undulation later than the first, the cord will 
take the form of a circular helix or cork-screw ; the 
extremity will move uniformly in a circle, and every 
molecule throughout the cord will do the same in suc- 
cession. It appears, therefore, that both circular and 
elliptical polarization may be produced, by the compo- 
sition of the motions of two rays in which the particles 
cf ether vibrate in places at right angles to one another. 

Professor Airy, in a very profound and able paper 
published in the Cambridge Transactions, has proved 
that all the different kinds of polarized light are obtained 
from rock crystal. When polarized light is transmitted 
through the axis of a crystal of quartz, in the emergent 
ray the particles of ether move in a circular helix; and 
when it is transmitted obliquely so as to form an angle 



SECT. XXII. ELLIPTICAL POLARIZATION. 187 

with the axis of the prism, the particles of ether move 
in an elliptical helix, the ellipticity increasing with the 
obliquity of the incident ray ; so that, when the incident 
ray falls perpendicularly to the axis, the particles of 
ether move in a straight line. Thus quartz exhibits 
every variety of elliptical polarization, even including 
the extreme cases where the eccentricity is zero, or 
equal to the greater axis of the ellipse (N. 210). In 
many crystals the two rays are so little separated, that 
it is only from the nature of the transmitted light that 
they are known to have the property of double refrac- 
tion. M. Fresnel discovered by experiments on the 
properties of light passing through the axis of quartz, 
that it consists of two superposed rays, moving with 
different velocities ; and Professor Airy has shown, that 
in these two rays, the molecules of ether vibrate in 
similar ellipses at right angles to each other, but in dif- 
ferent directions ; that their ellipticity varies with the 
angle which the incident ray makes with the axis ; and 
that, by the composition of their motions, they produce 
all the phenomena of polarized light observed in quartz. 

It appears from what has been said, that the mole- 
cules of ether always perform their vibrations at right 
angles to the direction of the ray, but very differently in 
the various kinds of light. In natural light the vibrations 
are rectilinear, and in every plane. In ordinary polar- 
ized light they are rectilinear, but confined to one plane ; 
in circular polarization the vibrations are circular ; and 
in elliptical polarization the molecules vibrate in ellipses. 
These vibrations are communicated from molecule to 
molecule, in straight lines when they are rectilinear, in 
a circular helix when they are circular, and in an oval 
or elliptical helix when elliptical. 

Some fluids possess the property of circular polar- 
ization, as oil of turpentine ; and elliptical polarization, 
or something similar, seems to be produced by reflection 
from metallic surfaces. 

The colored images from polarized light arise from 
the interference of the rays (N. 211). MM. Fresnel 
and Arago found that two rays of polarized light inter- 
fere and produce colored fringes if they be polarized in 
the same plane, but that they do not interfere when 



188 FORMATION OF IMAGES. SECT. XXII. 

polarized in different planes. In all intermediate posi- 
tions, fringes of intermediate brightness are produced. 
The analogy of a stretched cord will show how this 
happens. Suppose the cord to be moved backward and 
forward horizontally at equal intervals ; it will be thrown 
into an undulating curve lying all in one plane. If to 
this motion there be superadded another similar and 
equal, commencing exactly half an undulation later than 
the first, it is evident that the direct motion every mole- 
cule will assume, in consequence of the first system of 
waves, will at every instant be exactly neutralized by 
the retrograde motion it would take in virtue of the 
second ; and the cord itself will be quiescent in conse- 
quence of the interference. But if the second system 
of waves be in a plane perpendicular to the first, the 
effect would only be to twist the rope, so that no inter- 
ference would take place. Rays polarized at right an- 
gles to each other may subsequently be brought into the 
same plane without acquiring the property of producing 
colored fringes ; but if they belong to a pencil the whole 
of which was originally polarized in the same plane, they 
will interfere. 

The manner in which the colored images are formed 
may be conceived, by considering that when polarized 
light passes through the optic axis of a doubly refracting 
substance, as mica, for example, it is divided into two 
pencils by the analyzing tourmaline ; and as one ray is 
absorbed there can be no interference. But when 
polarized light passes through the mica in any other 
direction, it is separated into two white rays, and these 
are again divided into four pencils by the tourmaline, 
which absorbs two of them ; and the other two, being 
transmitted in the same plane with different velocities, 
interfere and produce the colored phenomena. If the 
analysis be made with Iceland spar, the single ray pass- 
ing through the optic axis of the mica will be refracted 
into two rays polarized in different planes, and no in- 
terference will happen. But when two rays are trans- 
mitted by the mica, they will be separated into four by 
the spar, two of which will interfere to form one image, 
and the other two, by their interference, will produce 
the complementary colors of the other image, when the 



SKCT. XXII. DISCOVERY OF POLARIZATION. 189 

spar has revolved through 90 ; because, in such posi- 
tions of the spar as produce the colored images, only 
two rays are visible at a time, the other two being re- 
flected. When the analysis is accomplished by reflec- 
tion, if two rays are transmitted by the mica, they are 
polarized in planes at right angles to each other. And 
if the plane of reflection of either of these rays be at 
right angles to the plane of polarization, only one of 
them will be reflected, and therefore no interference 
can take place ; but in all other positions of the analy- 
zing plate both rays will be reflected in the same plane, 
and consequently will produce colored rings by their 
interference. 

It is evident that a great deal of the light we see must 
be polarized, since most bodies which have the power 
of reflecting or refracting light also have the power of 
polarizing it. The blue light of the sky is completely 
polarized at an angle of 74 from the sun in a plane 
passing through his center. 

A constellation of talent almost unrivaled at any 
period in the history of science, has contributed to the 
theory of polarization, though the original discovery of 
that property of light was accidental, and arose from an 
occurrence which like thousands of others would have 
passed unnoticed, had it not happened to one of those 
rare minds capable of drawing the most important in- 
ferences from circumstances apparently trifling. In 
1808, while M. Malus was accidently viewing with a 
doubly-refracting prism a brilliant sunset reflected from 
the windows of the Luxembourg palace in Paris, on 
turning the prism slowly round, he was surprised to 
see a very great difference in the intensity of the two 
images, die most refracted alternately changing from 
brightness to obscurity at each quadrant of revolution. 
A phenomenon so unlocked for induced him to investi- 
gate its cause, whence sprung one of the most elegant 
and refined branches of physical optics. 



190 OBJECTIONS REMOVED. SEC*. XXIII. 



SECTION XXIII. 

Objections to the Undulatory Theory, from a Difference iu the Action of 
Sound and Light under the same circumstances, removed The Disper- 
sion of Light according to the Undulatory Theory. 

THE numerous phenomena of periodical colors arising 
from the interference of light, which do not admit of 
satisfactory explanation on any other principle than the 
undulatory theory, are the strongest arguments in favor 
of that hypothesis ; and even cases which at one time 
seemed unfavorable to that doctrine have proved upon 
investigation to proceed from it alone. Such is the er- 
roneous objection which has been made, in consequence 
of a difference in the mode of action of light and sound, 
under the same circumstances, in one particular in- 
stance. When a ray of light from a luminous point, 
and a diverging sound, are both transmitted through a 
very small hole into a dark room, the light goes straight 
forward and illuminates a small spot on the opposite wall, 
leaving the rest in darkness ; whereas the sound on en- 
tering diverges in all directions, and is heard in every 
part of the room. These phenomena, however, instead 
of being at variance with the undulatory theoiy, are 
direct consequences of it, arising from the very great 
difference between the magnitude of the undulations of 
sound and those of light. The undulations of light are 
incomparably less than the minute aperture, while those 
of sound are much greater. Therefore when light di- 
verging from a luminous point enters the hole, the rays 
round its edges are oblique, and consequently of different 
lengths, while those in the center are direct, and nearly 
or altogether of the same lengths. So that the small 
undulations between the center and the edges are in 
different phases, that is, in different states of undula- 
tion. Therefore the greater number of them interfere, 
and by destroying one another produce darkness all 
around the edges of the aperture ; whereas the central 
rays having the same phases, combine, and produce a 
spot of bright light on a wall or screen directly opposite 
the hole. The waves of air producing sound, on the 



SECT. XX1JI. OBJECTIONS REMOVED. 191 

contrary, being very large compared with the hole, da 
not sensibly diverge hi passing through it. and are there- 
fore all so nearly of the same length, and consequently 
in the same phase, or state of undulation, that none of 
them interfere sufficiently to destroy one another. 
Hence all the particles of air in the room are set into a 
state of vibration, so that the intensity of the sound is 
very nearly everywhere the same. Strong as the pre- 
ceding cases may be, the following experiment made by 
M. Arago about twenty years ago seems to be decisive 
in favor of the undulatory doctrine. Suppose a plano- 
convex lens of very great radius to be placed upon a 
plate of very highly polished metal. When a ray of 
polarized light falls upon this apparatus at a very great 
angle of incidence, Newton's rings are seen at the point 
of contact. But as the polarizing angle of glass differs 
from that of metal, when the light falls on the lens at 
the polarizing angle of glass, the black spot and the sys- 
tem of rings vanish. For although light in abundance 
continues to be reflected from the surface of the metal, 
not a ray is reflected from the surface of the glass that 
is in contact with it, consequently no interference can 
take place ; which proves, beyond a doubt, that New- 
ton's rings result from the interference of the light re- 
flected from both the surfaces apparently in contact (N. 
194). 

Notwithstanding the successful adaptation of the un- 
dulatory system to phenomena, the dispersion of light 
for a long time offered a formidable objection to that , 
theory, which has only been removed during the present 
year by Professor Powell of Oxford. 

A sunbeam falling on a prism, instead of being re- 
fracted to a single point of white light, is separated into 
its component colors, which are dispersed or scattered 
unequally over a considerable space, of which the portion 
occupied by the red rays is the least, and that over which 
the violet rays are dispersed is the greatest. Thus the 
rays of the colored spectrum whose waves are of differ- 
ent lengths, have different degrees of refrangibility, and 
consequently move with different velocities, either in the 
medium which conveys the light from the sun, or in the 
refracting medium, or in both ; whereas rays of all colors 



192 OBJECTIONS REMOVED. SECT. XXIII. 

come from the sun to the earth with the same velocity. 
If, indeed, the velocities of the various rays were differ- 
ent in space, the aberration of the fixed stars, which is 
inversely as the velocity, would be different for different 
colors, and every star would appear as a spectrum whose 
length would be parallel to the direction of the earth's 
motion, which is not found to agree with observation. 
Besides, there is no such difference in the velocities of 
the long and short waves of air in the analogous case of 
sound, since notes of the lowest and highest pitch are 
heard in the order in which they are struck. In fact, 
when the sunbeam passes from air into the prism its 
velocity is diminished ; and as its refraction and conse- 
quently its dispersion depend solely upon the diminished 
velocity of the transmission of its waves, they ought to 
be the same for waves of all lengths, unless a connection 
exists between the length of a wave, and the velocity 
with which it is propagated. Now this connection be- 
tween the length of a wave of any color and its velocity 
or refrangibility in a given medium, has been deduced 
by Professor Powell from M. Cauchy's investigations of 
the properties of light on a peculiar modification of the 
undulatory hypothesis. Hence the refrangibility of the 
various colored rays computed from this relation for any 
given medium, when compared with their refrangibility 
in the same medium determined by actual observation, 
will show whether the dispersion of light comes under 
the laws of that theory. But in order to accomplish 
this, it is clear that the length of the waves should be 
found independently of refraction, and a very beautiful 
discoveiy of M. Fraunhofer furnishes the means of 
doing so. 

That philosopher obtained a perfectly pure and com- 
plete colored spectrum with all its dark and bright lines 
by the interference of light alone, from a sunbeam pass- 
ing through a series of fine parallel wires covering the 
object glass of a telescope. In this spectrum, formed 
independently of prismatic refraction, the positions of 
the colored rays depend only on the lengths of their 
waves, and M. Fraunhofer found that the intervals be- 
tween them are precisely proportional to the differences 
of these lengths. He measured the lengths of the waves 



SICT. XXIV. OBJECTIONS REMOVED. 193 

of the different colors at seven fixed points, determined 
by seven of the principal dark and bright lines. Profes- 
sor Powell, availing himself of these measures, has made 
the requisite computations, and has found that the coin- 
cidence of theory with observation is perfect for ten 
substances whose refrangibility had been previously de- 
termined by the direct measurements of M. Fraunhofer, 
and for ten others whose refrangibility has more recently 
been ascertained by M. Rudberg, Thus, in the case of 
seven rays in each of twenty different substances solid 
and fluid, the dispersion of light takes place according to 
the laws of the undulatory theoiy; and as there can 
hardly be a doubt that dispersion hi all other bodies will 
be found to follow the same law, the undulatory theory 
of light may now be regarded as completely established. 
It is however an express condition of the connection be- 
tween the velocity of light and the length of its undula- 
tions, that the intervals between the vibrating molecules 
of the ethereal fluid should bear a sensible relation to 
the length of an undulation. The coincidence of the 
computed with the observed refractions shows that this 
condition is fulfilled within the refracting media ; but 
the aberration of the fixed stars leads to the inference 
that it does not hold in the ethereal regions, where the 
velocities of the rays of all colors are the same. 



SECTION XXIV. 

Chemical or Photographic Rays of the Solar Spectrum Messrs. Scheele, 
Ritter, and Wollaston's Discoveries Mr. Wedgewood and Sir Humphry 
Davy's Photographic Pictures The Calotype The Daguerreotype 
The Chromatype The Cyanotype Sir John Herschel's Discoveries in 
the Photographic or Chemical Spectrum Mons. E. Becquerel's Discovery 
of Inactive Lines in the Chemical Spectrum. 

THE solar spectrum has assumed a totally new char- 
acter from recent analysis, especially the chemical por- 
tion, which exercises an energetic action on matter, pro- 
ducing the most wonderful and mysterious changes on 
the organized and unorganized creation. 

All bodies are probably affected by light, but it acts 
with greatest energy on such as are of weak chemical 
affinity, imparting properties to them which they did 
13 R 



194 THE CALOTYPE. SECT. XXIV. 

not possess before. Metallic salts, especially those of 
silver, whose molecules are held together by an unstable 
equilibrium, are of all bodies the most susceptible of its 
influence ; the effects however vary with the substances 
employed and with the different rays of the solar spec- 
trum, the chemical properties of which are by no means 
alike. As early as 1772 M. Scheele showed that the 
pure white color of chloride of silver was rapidly dark- 
ened by the blue rays of the solar spectrum, while the 
red rays had no effect upon it; and in 1801 M. Hitter 
discovered that invisible rays beyond the violet extremity 
have the property of blackening argentine salts, that 
this property diminishes toward the less refrangible part 
of the spectrum, and that the red rays have an opposite 
quality, that of restoring the blackened saltaflfLsilver to 
its original purity, from which he inferredB3gthe most 
refrangible extremity of the spectrum ha^pn oxygen- 
izing power, and the other that of deoxygenating. Dr. 
Wollaston found that gum guaiacum acquires a green 
color in the violet and blue rays, and resumes its original 

fin the red. No attempt had been made to trace 
ural objects by means of light reflected from them 
Mr. Wedgewood, together with Sir Humphry Davy, 
took up the subject: they produced profiles and tracings 
of objects on surfaces prepared with nitrate and chloride 
of silver, but they did not succeed in rendering their 
pictures permanent. This difficulty was overcome in 
1814 by M. Niepce, who produced a permanent picture 
of surrounding objects, by placing in the focus of a 
camera obscura, a metallic plate covered with a film of 
asphalt dissolved in oil of lavender. 

MA Fox Talbot, without any knowledge of M. Niepce's 
experiments, had been engaged in the same pursuit, 
and -must be regarded as an independent inventor of 
photography, one of the most beautiful arts of modern 
times : he was the first who succeeded in using paper 
chemically prepared for receiving impressions from nat- 
ural objects ; and he also discovered a method of fixing 
permanently the impressions that is, of rendering the 
paper insensible to any further action of light. In the 
calotypo, one of Mr. Talbot's most recent applications 
of the art, this photographic surface is prepared by wash- 



SCT. XXIV. M. DAGUERRE 195 

ing smooth writing-ffoper, first with a solution of nitrate 
of silver, then with bromide of potassium, and again with 
nitrate of silver, drying it at a fire after each washing ; 
the paper is thus rendered so sensitive to light that even 
the passage of a thin cloud is perceptible on it, conse- 
quently it must be prepared by candle-light. Portraits, 
buildings, insects, leaves of plants, in short every object 
is accurately delineated in a few seconds, and in the 
focus of a camera obscura the most minute objects are 
so exactly depicted that the microscope reveals new 
beauties. 

Since the effect of the chemical agency of light is to 
destroy the affinity between the salt and the silver, Mr. 
Talbot found that in order to render these impressions 
permanent^pn paper, it was only necessary to wash it 
with saJBB water, or with a solution of iodide of po- 
tassiunaf^Wr these liquids the liquid hyposulphites 
have been* advantageously substituted, which are the 
most efficacious in dissolving and removing the unchanged 
salt, leaving the reduced silver on the paper. The cal- 
otype picture is negative, that is, the lights and shadows 
are the reverse of what they are in nature, and {& 
right-hand side in nature is the left in the picture ; but 
if it be placed with its face pressed against photographic 
paper, between a board and a plate of glass, and exposed 
to the sun a short time, a positive and direct picture as 
it is in nature is formed ; engravings may be exactly 
copied by this simple process, and a direct picture may 
be produced at once by using photographic paper already 
made brown by exposure to light. 

While Mr. Fox Talbot was engaged in these very 
elegant discoveries in England, M. Daguerre had brought 
to perfection and made public that admirable process by 
which he has compelled Nature permanently to en- 
grave her own works ; and thus the talents of France 
and England have been combined in bringing to perfec- 
tion this useful art. Copper, plated with silver, is suc- 
cessfully employed by M. Daguerre for copying nature 
by the agency of light. The surface of the plate is 
converted into an iodide of silver, by placing it horizon- 
tally with its face downward in a covered box, in the 
bottom of which there is a, small quantity of iodine 



196 THE CHROMATYPE. Scr. XXiV. 

which evaporates spontaneously. In three or four 
minutes the surface acquires a yellow tint, and then, 
screening it carefully from light, it must be placed in 
the focus of a camera obscura, where an invisible image 
of external objects will be impressed on it in a few 
minutes. When taken out the plate must be exposed 
in another box to the action of mercurial vapor, which 
attaches itself to those parts of the plate which had 
been exposed to light, but does not adhere to such parts 
as had been in shadow ; and as the quantity of mercury 
over the other parts is in exact proportion to the de- 
gree of illumination, the shading of the picture is per- 
fect. The image is fixed, first by removing the iodine 
from the plate, by plunging it into hyposulphite of soda, 
and then washing it in distilled water ; by this process 
the yellow color is destroyed, and in order to render 
the mercury permanent, the plate must be exposed a 
few minutes to nitric vapor, then placed in nitric acid 
containing copper or silver in solution at a temperature 
of 61| of Fahrenheit for a short time, and lastly 
polished with chalk. This final part of the process is 
due to Dr. Berre, of Vienna. 

Nothing can be more beautiful than the shading of 
these chiar-oscuro pictures when objects are at rest, 
but the least motion destroys the effect ; the method 
therefore is more applicable to buildings than landscape. 
Color alone is wanting ; but the researches of Sir John 
Herschel give reason to believe that even this will ulti- 
mately be attained. 

The most perfect impressions of seaweeds, leaves of 
plants, feathers, &c., may be formed by bringing the 
object into close contact with a- sheet of photographic 
paper, between a board and plate of glass ; then ex- 
posing the whole to the sun for a short time, and after- 
ward fixing it by the process described. The colors of 
the pictures vary with the preparation of the paper, by 
which almost any tint may be produced. 

In the chromatype, a peculiar photograph discovered 
by Mr. Hunt, chromate of copper is used, on which a 
dark brown negative image is first formed, but by the 
continued action of light it is changed to a positive 
yellow picture on a white ground ; the farther effect 



SCT. XXIV. DISTRIBUTION OP CHEMICAL ENERGY. ] 97 

of light is checked by washing the picture in pure 
water. 

In cyanotypes, a class of photographs discovered by 
Sir John Herschel, in which cyanogen in its combina- 
tions with iron forms the ground, the pictures are 
Prussian blue and white. In the chrysotype of the 
same eminent philosopher, the image is first received 
on paper prepared with the ammonia-citrate of iron, 
and afterward washed with a neutral solution of gold. 
It is fixed by water acidulated with sulphuric acid, and 
lastly by hydriodate of potash, from which a white and 
purple photograph results. It is vain to attempt to de- 
scribe the various beautiful effects which Sir John 
Herschel obtained from chemical compounds, and from 
the juices of plants : the juice of the red poppy gives a 
positive bluish purple image, that of the ten-week stock 
a fine rose color on a pale straw-colored ground. 

Pictures may be made by exposure to sunshine, on 
all compound substances having a weak chemical affinity, 
but the image is often invisible, as in the Daguerreotype, 
till brought out by washing in some chemical prepara- 
tion. Water is frequently sufficient ; indeed Sir John 
Herschel brought out dormant photographs by breathing 
on them, and some substances are insensible to the ac- 
tion of light till moistened, as for example gum guaia- 
cum. Argentine papers, however, are little subject to 
the influence of moisture. The power of the solar rays 
is augmented in certain cases by placing a plate of glass 
in close contact over the sensitive surface. 

Chemical action always accompanies the sun's light, 
but the analysis of the solar spectrum has partly dis- 
closed the wonderful nature of the emanation. In the 
research, properties most important and unexpected 
have been discovered by Sir John Herschel, who im- 
prints the stamp of genius on all he touches his elo- 
quent papers can alone convey an adequate idea of then? 
value in opening a field of inquiry vast and untrodden. 
The following brief and imperfect account of his exper- 
iments is all that can be attempted here : 

A certain degree of chemical energy is distributed 
through every part of the solar spectrum, and also to a 
considerable extent through the dark spaces at each ex- 



198 INTENSITY OF CHEMICAL ACTION. SECT. XXIV. 

tremity. This distribution does not depend on the re- 
frangibility of the rays alone, but also on the nature of 
the rays themselves, and on the physical properties of 
the analyzing medium on which the rays are received, 
whose changes indicate and measure their action. The 
length of the photographic image of the same solar spec- 
trum varies with the physical qualities of the surface on 
which it is impressed. When the solar spectrum is 
received on paper prepared with bromide of silver, the 
chemical spectrum, as indicated merely by the length of 
the darkened part, includes within its limits the whole 
luminous spectrum, extending in one direction far be- 
yond the extreme violet and lavender rays, and in the 
other down to the extremest red : with tartrate of sil- 
ver the darkening occupies not only all the space under 
the most refrangible rays, but reaches much beyond the 
extreme red. On paper prepared with formobenzoate 
of silver the chemical spectrum is cut off at the orange 
rays, with phosphate of silver in the yellow, and with 
chloride of gold it terminates with the green, with car- 
bonate of mercury it ends in the blue, and on paper 
prepared with the per cyanide of gold, ammonia, and 
nitrate of silver, the darkening lies entirely beyond the 
visible spectrum at its most refrangible extremity, and 
is only half its length, whereas in some cases chemical 
action occupies a space more than twice the length of 
the luminous image. 

The point of maximum energy of chemical action 
varies as much for different preparations as the scale of 
action. In the greater number of cases the point of 
deepest blackening lies about the lower edge of the in- 
digo rays, though in no two cases is it exactly the same, 
and in many substances it is widely different. On paper 
prepared with the juice of the ten-week stock (Mathiola 
annua), there are two maxima, one in the mean yellow 
and a weaker in the violet ; and on a preparation of tar- 
trate of silver, Sir John Herschel found three, one in 
the least refrangible blue, one in the indigo, and a third 
beyond the visible violet. The decrease in photographic 
energy is seldom perfectly alike on both sides of the 
maximum. Thus at the most refrangible end of the 
solar spectrum the greatest chemical power is exerted 



SBCT. XXIV. THE SOLAR SPECTRUM. 199 

in most instances where there fa least light and heat, 
and even in the space where both sensibly cease. 

Not only the intensity but the kind of action is differ- 
ent in the different points of the solar spectrum, as 
evidently appears from the various colors that are fre- 
quently impressed on the same analyzing surface, each 
ray having a tendency to impart its own color. Sir John 
Herschel obtained a colored image of the solar spectrum 
on paper prepared according to Mr. Talbot's principle, 
from a sunbeam refracted by a glass prism and then 
highly condensed by a lens. The photographic image 
was rapidly formed and very intense, and when with- 
drawn from the spectrum and viewed in common day- 
light it was found to be colored with sombre but une- 
quivocal tints imitating the prismatic colors, which varied 
gradually from red through green and blue^to a purplish 
black. After washing the surface in water, the tints 
became more decided by being kept a few days in the 
dark a phenomenon, Sir John observes, of constant 
occurrence, whatever be the preparation of the paper, 
provided colors are produced at all. He also obtained a 
colored image on nitrate of silver, the part under the 
blue rays becoming a blue brown, while that under the 
violet had a pinkish shade, and sometimes green ap- 
peared at the point corresponding to the least refrangible 
blue. Mr. Hunt found on a paper prepared with fluoride 
of silver that a yellow line was impressed on the space 
occupied by the yellow rays, a green band on the space 
under the green rays, an intense blue throughout the 
space on which the blue and indigo rays fell, and under 
the violet rays a ruddy brown appeared ; these colors 
remained clear and distinct after being kept two months. 

Notwithstanding the great variety in the scale of 
action of the solar spectrum, the darkening or deoxy- 
dizing principle that prevails in the more refrangible 
part rarely surpasses or even attains the mean yellow 
ray which is the point of maximum illumination ; it is 
generally cut off abruptly at that point which seems to 
form a limit between the opposing powers which prevail 
at the two ends of the spectrum. The bleaching or ox- 
ydizing effect of the red rays on blacke'ned muriate of 
silver discovered by M. Ritter of Jena, and the resfora- 



200 CHEMICAL SPECTRUM. SECT. XXIV. 

tion by the same rays of discolored gum guaiacum to its 
original tint by Dr. YVollaston, have already been men- 
tioned as giving the first indications of that difference in 
the mode of action of the chemical rays at the two ends 
of the visible spectrum, now placed beyond a doubt. 

The action exerted by the less refrangible rays be- 
yond and at the red extremity of the solar spectrum, in 
most instances, so far from blackening metallic salts, 
protects them from the action of the diffused daylight; 
but if the prepared surface has already been blackened 
by exposure to the sun, they possess the remarkable 
property of bleaching it in some cases, and under other 
circumstances of changing the black surface into a fiery 
red. 

Sir John Herschel, to whom we owe most of our 
knowledge of the properties of the chemical spectrum, 
prepared a sheet of paper by washing it with muriate 
of ammonia, and then with two coats of nitrate of silver ; 
on this surface he obtained an impression of the solar 
spectrum exhibiting a range of colors very nearly cor- 
responding with its natural hues. But a very remarka- 
ble phenomenon occurred at the end of least refrangi- 
bility ; the red rays exerted a protecting influence 
which preserved the paper from the change which it 
would otherwise have undergone from the deoxydizing 
influence of the dispersed light which always surrounds 
the solar spectrum, and this maintained its whiteness. 
Sir John met with another instance on paper prepared 
with bromide of silver, on which the whole of the space 
occupied by the visible spectrum was darkened down to 
the very extremity of the red rays, but an oxydizing 
action commenced beyond the extreme red, which main- 
tained the whiteness of the paper to a considerable dis- 
tance beyond the last traceable limit of the visible rays, 
thus evincing decidedly the existence of some chemical 
power over a considerable space beyond the least re- 
frangible end of the spectrum. Mr. Hunt also found 
that on the Daguerreotype plate a powerful protecting 
influence is exercised by the extreme red rays. In 
these cases the red and those dark rays beyond them 
exert an action -of an opposite nature to that of the violet 
and lavender ravs. 



Sicr.XXIV. BLEACHING POWER OF SOLAR SPECTRUM. 201 

The least refrangible part of the solar spectrum pos- 
sesses also, under certain circumstances, a bleaching 
property, by which the metallic salts are restored to 
their original whiteness after being blackened by ex- 
posure to common daylight, or to the most refrangible 
rays of the solar spectrum. 

Paper prepared with iodide of silver, when washed 
over with ferrocyanite of potash, blackens Vapidly when 
exposed to the solar spectrum. It begins in the violet 
rays and extends over all the space occupied by the dark 
chemical rays, and over the whole visible spectrum 
down to the extreme red rays. This image is colored, 
the red rays giving a reddish tint and the blue a bluish. 
In a short time a bleaching process begins under the red 
rays, and extends upward to the green, but the space 
occupied by the extreme red is maintained perfectly dark. 
Mr. Hunt found that a similar bleaching power is exerted 
by the red rays on paper prepared with protocyanide of 
potassium and gold with a wash of nitrate of silver. 

The application of a moderately strong hydriodate of 
potash to darkened photographic paper renders it pecu- 
liarly susceptible of "being whitened by further exposure 
to light. If paper prepared with bromide of silver be 
washed with ferrocyanate of potash while under the 
influence of the solar spectrum, it is immediately dark- 
ened throughout the part exposed to the visible rays 
down to the end of the red, some slight interference 
being perceptible about the region of the orange and 
yellow. After this a bleaching action begins over the 
part occupied by the red rays, which extends to the 
green. By longer exposure an oval spot begins again to 
darken about the center of the bleached space ; but if 
the paper receive another wash of the hydriodate of 
potash, the bleaching action extends up from the green, 
over the region occupied by the most refrangible rays 
and considerably beyond them, thus inducing a negative 
action in the most refrangible part of the spectrum. 

In certain circumstances the red rays, instead of re- 
storing darkened photographic paper to its original 
whiteness, produce a deep red color. When Sir John 
Herschel received the spectrum on paper somewhat 
discolored by exposure to direct sunshine, instead of 



202 PHOTOGRAPHY. SECT. XXIV. 

whiteness, a red border was formed extending from the 
space occupied by the orange, and nearly covering that 
on which the red fell. When, instead of exposing the 
paper in the first instance to direct sunshine, it was 
blackened by the violet rays of a prismatic spectrum, or 
by a sunbeam that had undergone the absorptive action 
of a solution of ammonia-sulphate of copper, the red 
rays of the condensed spectrum produced on it, not 
whiteness, but a full and fiery red which occupied the 
whole space on which any of the visible red rays had 
fallen, and this red remained unchanged, however long 
the paper remained exposed to the least refrangible rays. 

Sunlight transmitted through red glass produces the 
same effect as the red rays of the spectrum in the fore- 
going experiment. Sir John Herschel placed an en- 
graving over a paper blackened by exposure to sunshine, 
covering the whole with a dark red-brown glass previ- 
ously ascertained to absorb every ray beyond the orange : 
in this way a photographic copy was obtained in which 
the shades were black, as in the original engraving, but 
the lights, instead of being white, were of the red color 
of venous blood, and no other color could be obtained by 
exposure to light, however long. Sir John ascertained 
that every part of the spectrum impressed by the more 
refrangible rays is equally reddened, or nearly so, by the 
subsequent action of the less refrangible ; thus the red 
rays have the very remarkable property of assimilating 
to their own color the blackness already impressed on 
photographic paper. 

That there is a deoxy dating property in the more re- 
frangible rays, and an oxydating action in the less re- 
frangible part of the spectrum, is manifest from the 
blackening of one and the bleaching effect of the other ; 
but the peculiar action of the red rays in the experi- 
ments mentioned, shows that some other principle exists 
different from contrariety of action. These opposite 
qualities are balanced or neutralized in the region of the 
mean yellow ray. But although this is the general 
character of the photographic spectrum, under certain 
circumstances even the red rays have a deoxydating 
power, while the blue and scarlet exert a contrary influ- 
ence ; but these are rare exceptions. - 



S.CT. XXIV. REFRANGIBILITY. 203 

The photographic action of the two portions of the 
solar spectrum being so different, Sir John Herschel 
tried the effect of their united action by superposing the 
less refrangible part of the spectrum over the more re- 
frangible portion by means of two prisms, and he thus 
discovered that two rays of different refrangibility, and 
therefore of different lengths of undulation, acting simul- 
taneously, produce an effect which neither acting sepa- 
rately can do. 

Some circumstances that occurred during the analysis 
of the chemical spectrum seem to indicate an absorptive 
action in the sun's atmosphere. The spectral image 
impressed on paper prepared with nitrate of silver and 
Rochelle salt, commenced at or very little below the 
mean yellow ray, of a delicate lead color, and when tha 
action was arrested such was the character of the whole 
photographic spectrum. But when the light of the 
solar spectrum was allowed to continue its action, there 
was observed to come on suddenly a new and much 
more intense impression of darkness, confined in length 
to the blue and violet rays ; and what is most remarka- 
ble, confined also in breadth to the middle of the sun's 
image, so far at least as to leave a border of the lead- 
colored spectrum traceable, not only round the clear 
and well-defined convexity of the dark interior spectrum 
at the least refrangible end, but also laterally along both 
its edges : and this border was the more easily traced 
and less liable to be mistaken from its striking contrast 
of color with the interior spectrum, the former being 
lead gray, the latter an extremely rich deep velvety 
brown. The less refrangible end of this interior brown 
spectrum presented a sharply terminated and regularly 
elliptical contour, the more refrangible a less decided 
one. " It may seem too hazardous," Sir John continues, 
" $o look for the cause of this very singular phenomenon 
in a real difference between the chemical agencies of 
those rays which issue from the central portion of the 
sun's disc, and those which, emanating from its borders, 
have undergone the absorptive action of a much greater 
depth of its atmosphere ; and yet I confess myself some- 
what at a loss what other cause to assign for it. It 
must suffice, however, to have thrown out the hint, re- 



204 PHOTOGRAPHIC PHENOMENA. SKCT. XXIV. 

marking only, that I have other, and I am disposed to 
think decisive, evidence of the existence of an absorptive 
solar atmosphere extending beyond the luminous one." 
Several circumstances concur in showing that there are 
influences also concerned in the transmission of the pho- 
tographic action which have not yet been explained, as 
for example the influence which the time of the day 
exercises on the rapidity with which photographic im- 
pressions are made, the sun being much less effective 
two hours after passing the meridian than two hours 
before. There is also reason to Nsuspect that the effect 
in some way depends on the latitude, since a much 
longer time is required to obtain an image under the 
bright skies of the tropics than in England, and it is 
even probable that there is a difference in the sun's 
light in high and low latitudes, because an image of the 
solar spectrum obtained on a Daguerreotype plate in 
Virginia by Dr.- Draper, differed from a spectral image 
obtained by Mr. Hunt on a similar plate in England. 
The inactive spaces discovered in the photographic spec- 
trum by M. E. Becquerel similar to those in the lumi- 
nous spectrum, and coinciding with them, is also a phe- 
nomenon of which no explanation has yet been given. 
Although chemical action extends over the whole lumi- 
nous spectrum and much beyond it in gradations of 
more or less intensity, it is found by careful investiga- 
tion to be by no means continuous ; numerous inactive 
lines cross it coinciding with those in the luminous image 
as far as it extends : besides, a very great number exist 
in the portions that are obscure, and which overlap the 
visible part. There are three extra-spectral lines be- 
yond the red, and some strongly marked groups on the 
obscure part beyond the violet ; but the whole number 
of those inactive lines, especially in the dark spaces, is 
so great that it is impossible to count them. 

Notwithstanding this coincidence in the inactive lines 
of the two spectra, photographic energy is independent 
of both light and heat, since it exerts the most powerful 
influence in those rays where they are least, and also 
in spaces where neither sensibly exist ; but the trans- 
mission of the sun's light through colored media makes 
that independence quite evident. Heat and light pass 



SKUT. XXIV. PHOTOGRAPHIC PHENOMENA. ',205 

abundantly through yellow glass, or a solution of chro- 
mate of potash ; but the greater part of the chemical 
rays are excluded, and chlorine gas diluted with common 
air, though highly pervious to the luminous and calorific 
principles, has the same effect. Sir John Herschel 
found that a slight degree of yellow London fog had a 
similar effect with that of pale yellow media : he also 
remarked that a weak solution of azolitmine in potash, 
which admits a great quantity of green light, excludes 
chemical action ; and some years ago, the author, while 
making experiments on the transmission of chemical 
rays, observed that green glass, colored byoxyde of cop- 
per, about- the 20th of an inck thick, excludes the pho- 
tographic rays, and as M. Melloni has shown that sub- 
stance to be impervious to the most refrangible calorific 
rays, it has the property of excluding the whole of the 
most refrangible part of the solar spectrum, visible and 
invisible. Green mica, if not too thin, has also the same 
effect, whereas amethyst, deep blue and violet-colored 
glasses, though they transmit a very little light, allow 
the chemical rays to pass freely. Thus light and pho- 
tographic energy may be regarded as distinct and inde- 
pendent properties of the solar beam. 

It is not known whether photographic energy be ab- 
sorbed by material substances or not, neither is it known 
whether it be concerned in crystalization, and in pro- 
ducing those changes in the internal structure of cfystals 
when exposed to the sun, already mentioned ; but the 
power is universal wherever the solar beam falls, though 
the effect only becomes evident in cases of unstable mo- 
lecular equilibrium. The composition and decomposi- 
tion of those solids, liquids, and ae'riform fluids hitherto 
attributed to light, are chiefly owing to this energy ; and 
as similar chemical changes may be produced by cur- 
rents of electricity, an occult connection between these 
two imponderable influences is shadowed out, 
8 



206 HEAT SECT. XXV. 



SECTION XXV. 

Heat Calorific Rays of the Solar Spectrum Experiments of MM. De 
Laroche and Melloni on the Transmission of Heat The Point of greatest 
Heat in the Solar Spectrum varies with the Substance of the Prism 
Polarization of Heat Circular Polarization of Heat Transmission of the 
Chemical Rays Absorption of Heat Radiation of Heat Dew Hoar 
Frost Rain Hail Combustion Dilatation of Bodies by Heat Propa- 
gation of Heat Latent Heat Heat presumed to consist of the Undula- 
tions of an Elastic Medium Parathermic Rays Moser's Discoveries. 

IT is not by vision alone that a knowledge of the sun's 
rays is acquired, touch proves that they have the 
power of raising the temperature of substances exposed 
to their action. Sir William Herschel discovered that 
rays of caloric which produce the sensation of heat, exist 
in the solar spectrum independently of those of light ; 
when he used a prism of flint-glass, he found the warm 
rays most abundant in the dark space a little beyond the 
red extremity of the spectrum that from thence they 
decrease toward the violet, beyond which they are in- 
sensible. It may therefore be concluded, that the ca- 
lorific rays vary in refrangibility, and that those beyond 
the extreme red are less refrangible than any rays of 
light. Since Sir William Herschel's time it has been 
discovered that the calorific spectrum exceeds the lumi- 
nous one in length in the ratio of 42 to 25, but the most 
singular phenomenon of the calorific spectrum is its 
want of continuity. Sir John Herschel blackened the 
under side of a sheet of very thin white paper by the 
smoke of a lamp, and having exposed the white side to 
the solar spectrum, he drew a brush dipped in spirit of 
whie over it, by which the paper assumed a black hue 
when sufficiently saturated. The heat in the spectrum 
evaporated tha spirit first on those parts of the paper 
where it fell with greatest intensity, thereby restoring 
their white color, and thus he discovered that the ca- 
loric is not distributed uniformly, but in spots of greater 
or less intensity a circumstance probably owing to the 
absorbing action of the atmospheres of the sun and 
earth. " The effect of the former," says Sir John, u is 
beyond our control, unless we could carry our experi- 
ments to such a point of delicacy as to operate separately 



SKCT. XXV. SOLAR SPECTRUM. 207 

on rays emanating from the center and borders of the 
sun's disc ; that of the earth's, though it cannot be elim- 
inated any more than in the case of the sun's, may yet 
be varied to a considerable extent by experiments made 
at great elevations and under a vertical sun, and com- 
pared with others where the sun is more oblique, the 
situation lower, and the atmospheric pressure of a tem- 
porarily high amount. Should it be found that this 
cause is in reality concerned in the production of the 
spots, we should see reason to believe that a large por- 
tion of solar heat never reaches the earth's surface, and 
that what is incident on the summits of lofty mountains 
differs not only in quantity, but also in quality, from 
what the plains receive." 

Thus the solar spectrum is proved to consist of five 
superposed spectra, only three of which are visible 
the red, yellow, and blue; each of the five varies in 
refrangibility and intensity throughout the whole ex- 
tent, the visible part being overlapped at one extremity 
by the chemical, and at the other by the calorific rays ; 
but the two latter exceed the visible part so much, that 
the linear dimensions of the three, the luminous, calo- 
rific, and photographic, are in the proportion of the 
numbers 25, 42, 10, and 55-10, so that the whole solar 
spectrum is more than twice as long as its visible part. 

That the heat-producing rays exist independently of 
light, is a matter of constant experience in the abundant 
emission of them from boiling water. Yet there is 
every reason to believe that both the calorific and 
chemical rays are modifications of the same agent 
which produces the sensation of light. Rays of heat 
dart in diverging straight lines from flame, and from 
each point in the surfaces of hot bodies, in the same 
manner as diverging rays of light proceed from every 
point of the surfaces of such as are luminous. Accord- 
ing to the experiments of Sir John Leslie, radiation 
proceeds not only from the surfaces of substances, but 
also from the particles at a minute depth below it. He 
found that the emission is most abundant in a direction 
perpendicular to the radiating surface, and that it is 
more rapid from a rough than from a polished surface : 
radiation, however, can only take place in air and in 



208 RADIATION. SECT. XXV. 

vacuo ; it is altogether imperceptible when the hot 
body is inclosed in a solid or liquid. Heated substances, 
when exposed to the open air, continue to radiate 
caloric till they become nearly of the temperature of 
the surrounding medium. The radiation is very rapid 
at first, but diminishes according to a known law with 
the temperature of the heated body. It appears, also, 
that the radiating power of a surface is inversely as its 
reflecting power ; and bodies that are most impermea- 
ble to heat radiate least. 

Rays of heat, whether they proceed from the sun, 
from flame, or other terrestrial sources, luminous or 
non-luminous, are instantaneously transmitted through 
solid and liquid substances, there being no appreciable 
difference in the time they take to pass through layers 
of any nature or thickness whatever. They pass also 
with the same facility whether the media be agitated 
or at rest; and in these respects the analogy between 
light and heat is perfect. Radiant heat passes through 
the gases with the same facility as light ; but a remark- 
able difference obtains in the transmission of light and 
heat through most solid and liquid substances, the same 
body being often perfectly permeable to the luminous 
and altogether impermeable to the calorific rays. For 
example, thin and perfectly transparent plates of alum 
and citric acid sensibly transmit all the rays of light 
from an argand lamp, but stop eight or nine tenths of 
the concomitant heat ; while a large piece of brown 
rock crystal gives a free passage to the radiant heat, 
but intercepts almost all the light. M. Melloni has 
established the general law in uncrystalized substances 
such as glass and liquids, that the property of instanta- 
neously transmitting heat is in proportion to their re- 
fractive powers. The law, however, is entirely at fault 
in bodies of a crystaline texture. Carbonate of lead, 
for instance, which is colorless, and possesses a very 
high refractive power with regard to light, transmits 
less radiant heat than Iceland spar or rock-crystal, 
which are very inferior to it in the order of refran- 
gibility ; while rock-salt, which has the same transpa- 
rency and refractive power with alum and citric acid, 
transmits six or eight times as much caloric. This 



SICT. XXV. TRANSMISSION OP HEAT. 209 

remarkable difference in the transmissive power of sub- 
stances having the same- appearance, is attributed by M. 
Melloni to their crystaline form, and hot to the chemical 
composition of their molecules, as the following experi- 
ments prove. A block of common salt cut into plates, 
entirely excludes calorific radiation ; yet when dissolved 
in water, it increases the transmissive power of that 
liquid : moreover, the transmissive power of water is 
increased in nearly the same degree, whether salt or 
alum be dissolved in k ; yet these two substances 
transmit very different quantities of heat in their solid 
state. Notwithstanding the influence of ciy stall zation 
on the transmissive power of bodies, no relation has 
been traced between that power and the crystaline form. 
The transmission of radiant heat is analogous to that 
of light through colored media. When common white 
light, consisting of blue, yellow, and red rays, passes 
through a red liquid, almost all the blue and yellow rays, 
and a few of the red, are intercepted by the first layer 
of the fluid ; fewer are intercepted by the second, 
less by the third, and so on : till at last the losses ' 
very small and invariable, and those rays 
transmitted which give the red color to t 1 
a similar manner, when plates of the sair 
any substance, such as glass, are exposet 
lamp, a considerable portion of the rad 
rested by the first plate, a less port^- 
still less by the third, and so on, ' ' 
heat decreasing till at last the loss^ 
quantity. The traowmssion 
solid mass follows t ' @g f fie 
considerable on first 
ish in proportion as 
become constant at a certain 
difference between the transm> 
through a solid mass, or through the 
cut into plates of equal thickness, arises . 
quantity of heat that is reflected at the surface 
plates. It is evident, therefore, that the heat 
ually lost is not intercepted at the surface, but ab 
in the interior of the substance, and that heat 
has passed through one stratum of air experiences 
14 s2 



210 RADIANT HEAT. SECT. XXV. 

absorption in each of the succeeding strata, and may 
therefore be propagated to a greater distance before it 
is extinguished. The experiments of M. de Laroche 
show, that glass, however thin, totally intercepts the 
obscure rays of caloric when they flow from a body 
whose temperature is lower than that of boiling water ; 
that as the temperature increases, the calorific rays are 
transmitted more and more abundantly ; and when the 
body becomes highly luminous, that they penetrate the 
glass with perfect ease. The extreme brilliancy of the 
sun is probably the reason why his heat, when brought to 
a focus by a lens, is more intense than any that has been 
produced artificially. It is owing to the same cause 
that glass screens, which entirely exclude the heat of a 
common fire, are permeable by the solar caloric. 

The results obtained by M. de Laroche have been 

confirmed by the recent experiments of M. Melloni on 

caloric radiated from sources of different temperatures, 

whence it appears that the calorific rays pass less abun- 

*iy not only through glass, but through rock-crystal, 

spar, and other diaphanous bodies, both solid 

according as the temperature of their origin 

and that they are altogether intercepted 

)erature is about that of boiling water. 

as proved that the heat emanating from 

i a bright flame consists of rays which 

other as much as the red, yellow, and 

,h constitute white light. This ex- 

v f the loss of heat as it penetrates 

H solid mass, or in passing 

for, of the different kinds of 

all are successively 

.re of the substance 

till those homogeneous rays 

ve the greatest facility in passing 

aeuiar substance ; exactly as in a red 

and yellow rays are extinguished, and 

are transmitted. 

Melloni employed four sources of caloric, two of 
were luminous and two obscure ; namely, an oil- 
without u glass, incandescent platina, copper 
to 696, and a copper vessel filled with water at 



SCT.XXV. MELLONI'S EXPERIMENTS. 211 

the temperature of 178^ of Fahrenheit. Rock-salt 
transmitted heat in the proportion of 92 rays out of 
100 from each of these sources; but all other sub- 
stances pervious to radiant heat, whether solid or 
liquid, transmitted more caloric from sources of high 
temperature than from such as are low. For instance, 
limpid and colorless fluate of lime transmitted in the pro- 
portion of 78 rays out of 100 from the lamp, 69 from 
the platiua, 42 from the copper, and 33 from the hot 
water; while transparent rock-crystal transmitted 38 
rays in 100 from the lamp. 28 from the platina, 6 
from the copper, and 9 from the hot water. Pure ice 
transmitted only in the proportion of 6 rays in tbte 100 
from the lamp, and entirely excluded those from the 
other three sources. Out of 39 different substances, 
34 were pervious to the calorific rays from hot water, 
14 excluded those from the hot copper, and 4 did not 
transmit those from the platina. 

Thus it appears that heat proceeding from these 
sources is of different kinds : this difference in 
ture of the calorific rays is also proved by another, 
periment, which will be more easily understood from 
the analogy of light. Red light emanating from red 
glass, will pass in abundance through another piece of 
red glass, but it will be absorbed by green glass : green 
rays will more readily pass through a green medium 
than through one of any other color. This holds with 
regard to all colors; so in heat. Rays of caloric of the 
same intensity, which have passed through different 
substances, are transmitted in different quantities by the 
same piece of alum, and are sometimes stopped alto- 
gether ; showing that rays which emanate from different 
substances possess different qualities. It appears that 
a bright flame furnishes rays of heat of all kinds, in the 
same manner as it gives light of all colors ; and as col- 
ored media transmit some colored rays and absorb the 
rest, so bodies transmit some ray of caloric and ex- 
clude the others. Rock-salt alone resembles colorless 
transparent media in transmitting all kinds of caloric, 
even the heat of the hand, just as they transmit white 
light, consisting of rays of all colors. 

The property of transmitting the calorific rays di- 



ese tour 
th im- 
:h..-r ex- 



210 MELLONI'S EXPERIMENTS. SCT. XXV. 

rainishes to a certain degree with the thickness of the 
body they have to traverse, but not so much as might 
be expected. A piece of veiy transparent alum trans- 
mitted three or four times less radiant heat from the 
flame of a lamp than a piece of nearly opaque quartz 
about a hundred times as thick. However, the influ- 
ence of thickness upon the phenomena of transmission 
increases with the decrease of temperature in the 
origin of the rays, and becomes very great when that 
temperature is low. This is a circumstance intimately 
connected with the law established by M. de Laroche ; 
for M. Melloni observed that the difference between 
the quantities of caloric transmitted by the same plate 
of glass, exposed successively to several sources of heat, 
diminished with the thinness of the plate, and vanished 
altogether at a certain limit; and that a film of mica 
transmitted the same quantity of caloric, whether it 
was exposed to incandescent platina or to a mass of iron 
heated to 360. 

Colored glasses transmit rays of light of certain 
degrees of refrangibility, and absorb those of other 
degrees. For example, red glass absorbs the more 
refrangible rays, and transmits the red, which are the 
least refrangible. On the contrary, violet glass absorbs 
the least refrangible, and transmits the violet, which 
are the most refrangible. Now M. Melloni has found, 
that although the coloring matter of glass diminishes its 
power of transmitting heat, yet red, orange, yellow, 
blue, violet, and white glass transmit calorific rays of all 
degrees of refrangibility. Whereas green glass possesses 
the peculiar property of transmitting the least refrangi- 
ble calorific rays, and stopping those that are most re- 
frangible. It has therefore the same elective action 
for heat that colored glass has for light, and its action 
on heat is analogous to that of red glass on light. Alum 
and sulphate of lime are exactly opposed to green glass 
in their action on heat, by transmitting the most re- 
frangible rays with the greatest facility. 

The heat which has already passed through green or 
opaque black glass will not pass through alum, while 
that which has been transmitted through , glasses of 
other colors traverses it readily. 



SKCT. XXV. MELLONl'S EXPERIMENTS. 213 

By reversing the experiment, and exposing different 
substances to caloric that had already passed through 
alum, M. Melloni found that the heat emerging from 
alum is almost totally intercepted by opaque substances, 
and is abundantly transmitted by all such as are trans- 
parent and colorless, and that it suffers no appreciable 
loss when the thickness of the plate is varied within 
certain limits. The properties of the heat therefore 
which issues from alum, nearly approach to those of 
light and solar heat. 

Radiant heat in traversing various media is not only 
rendered more or less capable of being transmitted a 
second time, but, according to the experiments of Pro- 
fessor Powell, it becomes more or less susceptible of 
being absorbed in different quantities by black or v white 
surfaces. 

M. Melloni has proved. that solar heat contains rays 
which are affected by different substances in the same 
way as if the heat proceeded from a terrestrial source ; 
whence he concludes that the difference observed be- 
tween the transmission of terrestrial and solar heat 
arises from the circumstances of solar heat containing all 
kinds of caloric, while in other sources some of the kinds 
are wanting. 

Radiant heat, from sources of any temperature what- 
ever, is subject to the same laws of reflection and re- 
fraction as rays of light. The index of refraction from 
a prism of rock-salt determined experimentally, is nearly 
the same for light and heat. 

Liquids, the various kinds of glass, and probably all 
substances, whether solid or liquid, that do not crystal- 
ize regularly, are more pervious to the calorific rays 
according as they possess a greater refractive power. 
For example, the chloride of sulphur, which has a high 
refractive power, transmits more of the calorific rays than 
the oils, which have a less refractive power : oils trans- 
mit more radiant heat than the acids ; the acids more 
than aqueous solutions ; and the latter more than pure 
water, which of all the series has the least refractive 
power, and is the least pervious to heat. M. Melloni 
observed also, that each ray of the solar spectrum follows 
the same law of action with that of terrestrial rays hav- 



214 MAXIMUM OF HEAT IN SPECTRUM. SECT. XXV. 

ing their origin in sources of different temperatures ; so 
that the very refrangible rays may be compared to the 
heat emanating from a focus of high temperature, and 
the least refrangible to the heat which comes from a 
source of low temperature. Thus if the calorific rays 
emerging from a prism be made to pass through a layer 
of water contained between two plates of glass, it will 
be found that these rays suffer a loss in passing through 
the liquid, as much greater as their refrangibility is less. 
The rays of heat that are mixed with the blue or violet 
light pass in great abundance, while those in the obscure 
part which follows the red light are almost totally inter- 
cepted. The first, therefore, act like the heat of a 
lamp, and the last like that of boiling water. 

These circumstances explain the phenomena observed 
by several philosophers will regard to the point of 
greatest heat in the solar spectrum, which varies with 
the substance of the prism. Sir William Herschel, 
who employed a prism of flint glass, found that point to 
be a little beyond the red extremity of the spectrum : 
bat according to M. Seebeck, it is found to be upon the 
yellow, upon the orange, on the red, or at the dark 
limit of the red, according as the prism consists of 
water, sulphuric acid, crown or flint glass. If it be 
recollected that in the spectrum from crown glass, the 
maximum heat is in the red part, and that the solar 
rays, in traversing a mass of water, suffer losses inversely 
as their refrangibility, it will be easy to understand the 
reason of the phenomenon in question. The solar heat 
which comes to the anterior face of the prism of water 
consists of rays of all degrees of refrangibility. Now, 
the rays possessing the same index of refraction with 
the red light suffer a greater loss in passing through the 
prism than the rays possessing the refrangibility of the 
orange light, and the latter lose less in their passage than 
the heat of the yellow. Thus the losses, being inversely 
proportional to the degree of refrangibility of each ray, 
cause the point of maximum heat to tend from the red 
toward the violet, and therefore it rests upon the yellow 
part. The prism of sulphuric acid acting similarly, but 
with less energy than that of water, throws the point of 
greatest heat on the orange ; for the same reason, tho 



SECT. XXV POLARIZATION OF CALORIC. 215 

crown and flint glass prisms transfer that point respec- 
tively to the red and to its limit. M. Melloni, observing 
that the maximum point of heat is transferred farther 
and farther toward the red end of the spectrum, ac- 
cording as the substance of the prism is more and more 
permeable to heat, inferred that a prism of rock-salt, 
which possesses a greater power of transmitting the 
calorific rays than any known body, ought to throw the 
point of greatest heat to a considerable distance beyond 
the visible part of the spectrum, an anticipation which 
experiment fully confirmed, by placing it as much be- 
yond the dark limits of the red rays as the red part is 
distant from the bluish green band of the spectrum. 

In all these experiments, M. Melloni employed a 
thermo-multiplier, an instrument that measures the 
intensity of the transmitted heat with an accuracy far 
beyond what any thermometer ever attained. It is a 
very elegant application of M. Seebeck's discovery oi 
thermo-electricity; but the description of this instrument 
is reserved for a future occasion, because the principle 
on which it is constructed has not yet been explained. 

In the beginning of the present century, not long after 
M. Malus had discovered the polarization of light, he 
and M. Berard proved that the heat which accompanies 
the sun's light is capable of being polarized ; but their 
attempts totally failed with heat derived from terrestrial, 
and especially from non-luminous sources. M. Berard, 
indeed, imagined that he had succeeded ; but when his 
experiments were repeated by Mr. Lloyd and Professor 
Powell, no satisfactory result could be obtained. M- 
Melloni lately resumed the subject, and endeavored to 
effect the polarization of heat by tourmaline, as in the 
case of light. It was already shown that two slices of 
tourmaline cut parallel to the axis of the crystal, trans- 
mit a great portion of the incident light when looked 
through with their axes parallel, and almost entirely ex- 
clude it when they are perpendicular to one another. 
Should radiant heat be capable of polarization, the quan- 
tity transmitted by the slices of tourmaline in their for- 
mer position ought greatly to exceed that which passes 
through them in the latter, yet M. Melloni found that 
the quantity of heat was the same in both cases : whence 



216 POLARIZATION OF CALORIC. SECT. XXV. 

he inferred that heat from a terrestrial source is inca- 
pable of being polarized. Professor Forbes of Edin- 
burgh, who has recently prosecuted this subject with 
great acuteness and success, came to the same conclu- 
sion in the first instance ; but it occurred to him, that as 
the pieces of tourmaline became heated by being very 
near the lamp, the secondary radiation from them ren- 
dered the very small difference in the heat that was 
transmitted in the two positions of the tourmalines im- 
perceptible. The same conclusion had been come at 
by M. Melloni ; nevertheless Mr. Forbes succeeded in 
proving by numerous observations, that heat from vari- 
ous sources was polarized by the tourmaline ; but that 
the effect with non-luminous heat was very minute and 
difficult to perceive, on account of the secondary radia- 
tion. Though light is almost entirely excluded in one 
position of the tourmalines, and transmitted in the other, 
a vast quantity of radiant heat passes through them in 
all positions. Eighty-four per cent, of the heat from an 
argand lamp passed through the tourmalines in the case 
where light was altogether stopped. It is only the dif- 
ference in the quantity of transmitted heat that gives 
evidence of its polarization. The second slice of tour- 
maline, when perpendicular to the first, stops all the 
light, but transmits a great proportion of heat ; alum, on 
the contrary, stops almost all the heat and transmits the 
light ; whence it may be concluded that heat, though 
intimately partaking the nature of light, and accompany- 
ing it under certain circumstances, as in reflection and 
refraction, is capable of almost complete separation from 
it under others. The separation has since been per- 
fectly effected by M. Melloni, by passing a beam of light 
through a combination of water and green glass, colored 
by the oxide of copper. Even when the transmitted 
light was concentrated by lenses, so as to render it almost 
as brilliant as the direct light of the sun, it showed no 
sensible heat. 

Professor Forbes next employed two bundles of lam- 
inae of mica, placed at the polarizing angle, and so cut 
that the plane of incidence of the heat corresponded 
with one of the optic axes of this mineral. The heat 
transmitted through this apparatus was polarized when, 



SECT. XXV. POLARIZATION OF CALORIC. 217 

from a source whose temperature was even as low as 
200, heat was also polarized by reflection ; but the ex- 
periments, though perfectly successful, are more diffi- 
cult to conduct. 

It appears from the various experiments of M. Mel- 
loni and Professor Forbes, that all the calorific rays ema- 
nating from the sun and terrestrial sources are equally 
capable of being polarized by reflection and by refrac- 
tion, whether double or simple, and that they are also 
capable of circular polarization by all the methods em- 
ployed in the circular polarization of light. Plates of 
quartz cut at right angles to the axis of the prism, pos- 
sess the property of turning the calorific rays in any 
direction, while other plates of the same substance from 
a differently modified prism cause the rays to rotate in 
the contrary direction ; and two plates combined, when 
of different affection, and of equal thickness, counteract 
each other's effects, as in the case of light. Tourmaline 
separates the caloric into two parts, one of which it ab- 
sorbs, while it transmits the other ; in short, the trans- 
mission of radiant heat is precisely similar to that of light. 

Since heat is polarized in the same manner as light, it 
may be expected that polarized heat transmitted through 
doubly refracting substances should be separated into 
two pencils, polarized in planes at right angles to each 
other ; and that when received on an analyzing plate 
they should interfere and produce invisible phenomena, 
perfectly analogous to those described in Section XXII. 
with regard to light (N. 212). 

It was shown in the same section, that if light polar- 
ized by reflection from a pane of glass be viewed through 
a plate of tourmaline, with its longitudinal section verti- 
cal, an obscure cloud, with its center wholly dark, is 
seen on the glass. When, however, a plate of mica 
uniformly about the thirteenth of an Inch in thickness 
is interposed between the tourmaline and the glass, the 
dark spot vanishes, and a succession of very splendid 
colors is seen; and as the mica is turned round in a 
plane perpendicular to the polarized ray, the light is 
stopped when the plane containing the optic axis of the 
mica is parallel or perpendicular to the plane of polar- 
ization. Now instead of light, if heat from a non-lumi~ 



218 POLARIZATION OF CALORIC. SECT. XXV. 

nous source be polarized in the manner described, it 
ought td be transmitted and stopped by the interposed 
mica under the same circumstances under which polar- 
ized light would be transmitted or stopped. Prolessor 
Forbes has found that this is really the case, whether he 
employed heat from luminous or non-luminous sources : 
and he had evidence also of circular and elliptical polar- 
ization of heat. It therefore follows that if heat were 
visible, under similar circumstances we should see fig- 
ures perfectly similar to those given in Note 207, and 
those following; and as these figures are formed by the 
interference of undulations of light, it may be inferred 
that heat, like light, is propagated by undulations of the 
ethereal medium, which interfere under certain condi- 
tions, and produce figures analogous to those of light. 
It appears also from Mr. Forbes's experiments, that the 
undulations of heat are probably longer than the undu- 
lations of light. 

Since the power of penetrating glass increases in pro- 
portion as the radiating caloric approaches the slate of 
light, it seemed to indicate that the same principle takes 
the form of light or heat according to the modification 
it receives, and that the hot rays are only invisible light; 
and light, luminous caloric. It was natural to infer, that 
in the gradual approach of invisible caloric to the condi- 
tion and properties of luminous caloric, the invisible 
rays must at first be analogous to the least calorific part 
of the spectrum, which is at the violet extremity an 
analogy which appeared to be greater, by all flame 
being at first violet or blue, and only becoming white 
when it has attained its greatest intensity. Thus, as 
diaphanous bodies transmit light with the same facility 
whether proceeding from the sun or from a glowworm, 
and as no substance had hitherto been found which in- 
stantaneously transmits radiant caloric coming from a 
source of low temperature, it was concluded that no 
such substance exists, and the great difference between 
the transmission of light and radiant heat was thus re- 
ferred to the nature of the agent of heat, and not to the 
action of matter upon the calorific rays. M. Melloni, 
however, has discovered in rock-salt a substance which 
transmits radiant heat with the same facility whether it 



SBCT. XXV. NATURE OF CALORIC. 219 

originates in the brightest flame or lukewarm water, 
and which consequently possesses the same permeability 
with regard to heat that all diaphanous bodies have for 
light. It follows, therefore, that the impermeability of 
glass and other substances for radiant heat arises from 
their action upon the calorific rays, and not from the 
principle of caloric. But although this discovery changes 
the received ideas drawn from M. de Laroche's experi- 
ments, it establishes a new and unlooked-for analogy 
between these two great agents of nature. True it is 
that the separation of the luminous and calorific rays 
shows that they must owe their immediate origin to two 
different causes, at the same time it is quite possible 
that these two causes themselves may be only different 
effects of one single cause. The probability of light and 
heat being modifications of the same principle is not 
diminished by the calorific rays being unseen, for the 
condition of visibility or invisibility may only depend 
upon the construction of our eyes, and not upon the 
nature of the agent which produces these sensations in 
us. The sense of seeing may be confined within certain 
limits. The chemical rays beyond the violet end of the 
spectrum may be too rapid, or not sufficiently excursive 
in their vibrations to be visible to the human eye ; and 
the calorific rays beyond the other end of the spectrum 
may not be sufficiently rapid, or too extensive, in their 
undulations, to affect our optic nerves, though both may 
be visible to certain animals or insects. We are alto- 
gether ignorant of the perceptions which direct the car- 
rier-pigeon to his home, or of those in the antennae of 
insects which warn them of the approach of danger; 
nor can we understand the telescopic vision which di- 
rects the vulture to his prey before he himself is visible 
even as a speck in the heavens (N. 213). So likewise 
beings may exist on earth, in the air, or in the waters, 
which hear sounds our ears are incapable of hearing, 
and which see rays of light and heat of which we are 
unconscious. Our perceptions and faculties are limited 
to a very small portion of that immense chain of exist- 
ence which extends from the Creator to evanescence. 

The identity of action under similar circumstances is 
one of the strongest arguments in favor of the common 



220 ABSORPTION OF CALORIC. SECT. XXV. 

nature of the chemical, visible, and calorific rays. They 
are all capable of reflection from polished surfaces, of 
refraction through diaphanous substances, of polarization 
by reflection and by doubly refracting crystals : none of 
these rays add sensibly to the weight of matter; their 
velocity is prodigious ; they may be concentrated and 
dispersed by convex and concave mirrors ; they pass 
with equal facility through rock-salt, and are capable of 
radiation ; the chemical rays are subject to the same 
law of interference with those of light ; and although 
the interference of the calorific rays has not yet been 
proved directly, the indirect evidence places it beyond a 
doubt. As the action of matter in so many cases is the 
same on the whole assemblage of rays, visible and 
invisible, which constitute a solar beam, it is more than 
probable that the obscure as well as the luminous part is 
propagated by the undulations of an imponderable ether, 
and consequently comes under the same laws of analysis. 
When radiant heat falls upon a surface, part of it is 
reflected and part of it is absorbed ; consequently the 
best reflectors possess the least absorbing powers. The 
temperature of very transparent fluids is not raised by 
the passage of the sun's rays, because they do not 
absorb any of them : and as his heat is very intense, 
transparent solids arrest a very small portion of it. 
The absorption of the sun's rays is the cause both of 
the color and temperature of solid bodies. A black 
substance absorbs all the rays of light and reflects none; 
and since it absorbs at the same time all the calorific 
rays, it becomes sooner warm, and rises to a higher 
temperature than bodies of any other color. Blue 
bodies come next to black in their power of absorption. 
Of all the colors of the solar spectrum, the blue pos- 
sesses least of the heating power ; and since substances 
of a blue tint absorb all the other colors of the spectrum, 
they absorb by far the greatest part of the calorific rays, 
and reflect the blue where they are least abundant. 
Next in order come the green, yellow, red, and last of 
all, white bodies, which reflect nearly all the rays both 
of light and heat. However, there are certain limpid 
and colorless media, which in some cases intercept 
calorific radiations and become heated, while in other 



SECT. XXV. ABSORPTION OF CALORIC DEW. 221 

cases they transmit them and undergo no change of 
temperature. 

All substances may be considered to radiate caloric, 
whatever their temperature may be, though with dif- 
ferent intensities, according to their nature, the state of 
their surfaces, and the temperature of the medium into 
which they are brought. But eveiy surface absorbs as 
well as radiates caloric ; and the power of absorption 
is always equal to that of radiation ; for under the same 
circumstances, matter which becomes soon warm also 
cools rapidly. There is a constant tendency to an 
equal diffusion of caloric, since every body in nature is 
giving and receiving it at the same instant : each will be 
of uniform temperature when the quantities of caloric 
given and received during the same time are equal, 
that is, when a perfect compensation takes place be- 
tween each and all the rest. Our sensations only 
measure comparative degrees of heat: when a body, 
such as ice, appears to be cold, it imparts fewer calorific 
rays than it receives ^ and when a substance seems to 
be warm, for example, a fire, it gives more caloric 
than it takes. The phenomena of dew and hoar-frost 
are owing to this inequality of exchange ; the caloric 
radiated during the night by substances on the surface 
of the earth into a clear expanse of sky is lost, and no 
return is made from the blue vault, so that their tem- 
perature sinks below that of the air, whence they 
abstract a part of that caloric which holds the atmos- 
pheric humidity in solution, and a deposition of dew 
takes place. If the radiation be great, the dew is 
frozen and becomes hoar-frost, which is the ice of dew. 
Cloudy weather is unfavorable to the formation of dew, 
by preventing the free radiation of caloric ; and actual 
contact is requisite for its deposition, since it .is never 
suspended in the air like fog. Plants derive a great 
part of their nourishment from this source ; and as each 
possesses a power of radiation peculiar to itself, they 
are capable of procuring a sufficient supply for their 
wants. The action of the chemical rays imparts to all 
substances more or less the power of condensing vapor 
on tlwse parts on which they fall, and must therefore 
have a considerable influence on the deposition of dew. 

T2 



222 RAIN COMBUSTION. SECT. XXV. 

Ram is formed by the mixing of two masses of air of 
different temperatures; the colder part, by abstracting 
from the other the heat which holds it in solution, occa- 
sions the particles to approach each other and form 
drops of water, v which, becoming too heavy to be sus- 
tained by the atmosphere, sink to_ the earth by gravita- 
tion in, the form of rain. The contact of two strata of 
air of different temperatures, moving rapidly in opposite 
directions, occasions an abundant precipitation of rain. 
When the masses of air differ very much in tempera- 
ture, and meet suddenly, hail is formed. This happens 
frequently in hot plains near a ridge of mountains, as in 
the south of France ; but no explanation has hitherto 
been given of the cause of the severe hail-storms which 
occasionally take place on extensive plains within the 
tropics. 

An accumulation of caloric invariably produces light : 
with the ^exception of the gases, all bodies which can 
endure the requisite degree of heat without decompo- 
sition begin to emit light at the same temperature ; but 
when the quantity of caloric is so great as to render the 
affinity of their component particles less than their 
affinity for the oxygen of the atmosphere, a chemical 
combination takes place with the oxygen, light and heat 
are evolved, and fire is produced. Combustion so 
essential for our comfort, and even existence takes 
place very easily from the small affinity between the 
component parts of atmospheric air, the oxygen being 
nearly in a free state ; but as the cohesive force of the 
particles of different substances is very variable, differ- 
ent degrees of heat are requisite to produce their com- 
bustion. The tendency of heat to a state of equal 
diffusion or equilibrium, either by radiation or contact, 
makes it necessary that the chemical combination which 
occasions combustion should take place instantaneously ; 
for if the heat were developed progressively, it would 
be dissipated by degrees, and would never accumulate 
sufficiently to produce a temperature high enough for 
the evolution of flame. 

It is a general law that all bodies expand by heat and 
contract by cold. The expansive force of tfaloric has a 
constant tendency to overcome the attraction of cohesion, 



SICT. XXV. EXPANSION. 223 

and to separate the constituent particles of solids and 
fluids ; by this separation the attraction of aggregation is 
more and more weakened, till at last it is entirely over- 
come, or even changed into repulsion. By the continual 
addition of caloric, solids may be made to pass into liquids, 
and from liquids to the aeriform state, the dilatation in- 
creasing with the temperature ; and every substance ex- 
pands according to a law of its own. Gases expand more 
than liquids, and liquids more than solids. The expan- 
sion of air is more than eight times that of water, and the 
increase in the bulk of water is at least forty-five times 
greater than that of iron. Metals dilate uniformly from 
the freezing to the boiling points of the thermometer ; 
the uniform expansion of the gases extends between still 
wider limits ; but as liquidity is a state of transition from 
the solid to the ae'riform condition, the equable dilatation 
of liquids has not so extensive a range. This change of 
bulk, corresponding to the variation of heat, is one of the 
most important of its effects, since it furnishes the means 
of mejisuring relative temperature by the thermometer 
and pyrometer. The rate of expansion of solids varies 
at their transition to liquidity, and that of liquidity is no 
longer equable near their change to an aeriform state. 
There are exceptions however to the general laws of 
expansion ; some liquids have a maximum density corres- 
ponding to a certain temperature, and dilate whether that 
temperature be increased or diminished. For example 
water expands whether it be heated above or cooled 
below 40. Tha solidification of some liquids, and es- 
pecially their crystalization, is always accompanied by an 
increase of bulk. Water dilates rapidly when converted 
into ice, and with a force sufficient to split the hardest 
substances. The formation of ice is therefore a pow- 
erful agent in the disintegration and decomposition of 
rocks, operating as one of the most efficient causes of 
local changes in the structure of the crust of the earth ; 
of which we have experience in the tremendous eboule- 
tnents of mountains in Switzerland. 

The dilatation of substances by heat, and their con- 
traction by cold, occasion such irregularities in the rate 
of clocks and watches as would render them unfit for 
astronomical or nautical purposes, were it not for a very 



224 COMPENSATION PENDULUM. SECT. XXV. 

beautiful application of the laws of unequal expansion. 
The oscillations of a pendulum are the same as if its 
whole mass were united in one dense particle, in a cer- 
tain point of its length, called the center of oscillation. 
If the distance of this point from the point by which the 
pendulum is suspended were invariable, the rate of the 
clock would be invariable also. The difficulty is to neu- 
tralize the effects of temperature, which is perpetually 
increasing or diminishing its length. Among many con- 
trivances, Graham's compensation pendulum is the most 
simple. He employed a glass tube containing mercury. 
When the tube expands from the effects of heat, the 
mercury expands much more ; so that its surface rises 
a little more than the end of the pendulum is depressed, 
and the center of oscillation remains stationary. Har- 
rison invented a pendulum which consists of seven bars 
of steel and of brass, joined in the shape of a gridiron, 
in such a manner that if by change of temperature the 
bars of brass raise the weight at the end of the pendu- 
lum, the bars of steel depress it as much. In general, 
only five bars are used ; three being of steel and two a 
mixture of silver and zinc. The effects of temperature 
are neutralized in chronometers upon the same princi- 
ple ; and to such perfection are they brought, that the 
loss or gain of one second in twenty-four hours for two 
days running would render one unfit for use. Accuracy 
in surveying depends upon the compensation rods em- 
ployed in measuring bases. Thus, the laws of the une- 
qual expansion of matter judiciously applied have an 
immediate influence upon our estimation of time : of 
the motions of bodies in the heavens, and of their fall 
upon the earth ; on our determination of the figure of 
the globe, and on our system of weights and measures ; 
on our commerce abroad, and the mensuration of our 
lands at home. 

The expansion of the crystaline substances takes place 
under very different circumstances from the dilatation 
of such as are not crystalized. The latter become both 
longer and thicker by an acession of heat, whereas M. 
Mitscherlich has found that the former expand differ- 
ently in different directions ; and in a particular instance, 
extension in one direction is accompanied by contraction 



SECT. XXV. PROPAGATION OF HEAT. 225 

in another. The internal structure of crystalized mat- 
ter must be very peculiar, thus to modify the expansive 
power of heat, and so materially to influence the trans- 
mission of caloric and the visible rays of the spectrum. 

Heat is propagated with more or less rapidity through 
all bodies ; air is the worst conductor, and consequently 
mitigates the severity of cold climates by preserving the 
heat imparted to the earth by the sun. On the con- 
trary, dense bodies, especially metals, possess the power 
of conduction in the greatest degree, but the transmis- 
sion requires time. If a bar of iron twenty inches long 
be heated at one extremity, the caloric takes four min- 
utes in passing to the other. The particle of the metal 
that is first heated communicates its caloric to the sec- 
ond, and the second to the third ; so that the temperature 
of the intermediate molecule at any instant is increased 
by the excess of the temperature of the first above its 
own, and diminished by the excess of its own tempera- 
ture above that of the third. That however will not 
be the temperature indicated by the thermometer, be- 
cause as soon as the particle is more heated than the 
surrounding atmosphere, it loses its caloric by radiation, 
in proportion to the excess of its actual temperature 
above that of the air. The velocity of the discharge is 
directly proportional to the temperature, and inversely 
as the length of the bar. As there are perpetual varia- 
tions in the temperature of all terrestrial substances and 
of the atmosphere, from the rotation of the earth, and 
its revolution round the sun, from combustion, friction, 
fermentation, electricity, and an infinity of other causes, 
the tendency to restore the equability of temperature 
by the transmission of caloric must maintain all the 
particles of matter in a state of perpetual oscillation, 
which will be more or less rapid according to the con- 
ducting powers of the substances. From the motion of 
the heavenly bodies about then* axes, and also round the 
sun, exposing them to perpetual changes of temperature, 
it may be inferred that similar causes will produce like 
effects in them too. The revolutions of the double stars 
show that they are not at rest ; and though we are to- 
tally ignorant of the changes that may be going on in the 
nebulae and millions of other remote bodies, it is hardly 
15 



226 PROPAGATION OF HEAT. SECT. XXV. 

possible that they should be in absolute repose ; so that, 
as far as our knowledge extends, motion seems to be a 
law of matter. 

Heat applied to the surface of a fluid is propagated 
downward very slowly, the warmer and consequently 
lighter strata always remaining at the top. This is the 
reason why the water at the bottom of lakes fed from 
alpine chains is so cold ; for the heat of the sun is trans- 
fused but a little way below the surface. "When heat 
is applied below a liquid, the particles continually rise 
as they become specifically lighteir in consequence of 
the caloric, and diffuse it through the mass, their place 
being perpetually supplied by those that are more dense. 
The power of conducting heat varies materially in dif- 
ferent liquids. Mercury conducts twice as fast as an 
equal bulk of water, which is the reason why it appears 
to be so cold. A hot body diffuses its caloric in the ah* 
by a double process. The air in contact with it being 
heated and becoming lighter, ascends and scatters its 
caloric, while at the same time another portion is dis- 
charged in straight lines by the radiating powers of the 
surface. Hence a substance cools more rapidly in air 
than in vacuo, because in the latter case the process is 
carried on by radiation alone. It is probable that the 
earth, having originally been of very high temperature, 
has become cooler by radiation only. The ethereal 
medium must be too rare to carry off much caloric. 

Besides the degree of heat indicated by the thermom- 
eter, caloric pervades bodies in an imperceptible or latent 
state ; and their capacity for heat is so various, that veiy 
different quantities of caloric are required to raise differ- 
ent substances to the same sensible temperature ; it is 
therefore evident that much of the caloric is absorbed, 
or becomes latent and insensible to the thermometer. 
The portion of caloric requisite to raise a body to a given 
temperature is its specific heat ; but latent heat is that 
portion of caloric which is employed in changing the state 
of bodies from solid to liquid, and from liquid to vapor. 
When a solid is converted into a liquid, a greater quan- 
tity of caloric enters into it than can be detected by the 
thermometer ; this accession of caloric does not make 
the body warmer, though it converts it into a liquid, and 



SKCT. XXV. LATENT HEAT. 227 

is the principal cause of its fluidity. Ice remains at the 
temperature of 32 of Fahrenheit till it has combined 
with or absorbed 140 of caloric, and then it_melts, but 
without raising the temperature of the water above 32 ; 
so that water is a compound of ice and caloric. On 
the contrary, when a liquid is converted into a solid, a 
quantity of caloric leaves it without any diminution of 
temperature. Water at the temperature of 32 must 
part with 140 of caloric before it freezes. The slow- 
ness with which water freezes, or ice thaws, is a con- 
sequence of the time required to give out or absorb 140 
of latent heat. A considerable degree of cold is often felt 
during a thaw, because the ice, in its transition from a 
solid to a liquid state, absorbs sensible heat from the atmos- 
phere and other bodies, and by rendering it latent main- 
tains them at the temperature of 32 while melting. Ac- 
cording to the same principle, vapor is a combination of 
caloric with a liquid. By the continued application of 
heat, liquids are converted into vapor or steam, which 
is invisible and elastic like common air. Under the 
ordinary pressure of the atmosphere, that is, when the 
barometer stands at 30 inches, water acquires a constant 
accession of heat till its temperature rises to 212 of 
Fahrenheit ; after that it ceases to show any increase 
in heat, but when it has absorbed an additional 1000 of 
caloric it is converted into steam. Consequently, about 
1000 of latent heat exists in steam without raising its 
temperature, and steam at 212 must part with the same 
quantity of latent caloric when condensed into water. 
Water boils at different temperatures under different 
degrees of pressure. It boils at a lower temperature 
on the top of a mountain than in the plain below, 
because the weight of the atmosphere is less at the 
higher station. There is no limit to the temperature 
to which water might be raised ; it might even be made 
red-hot, could a vessel be found strong enough to resist 
the pressure. The expansive force of steam is in pro- 
portion to the temperature at which the water boils ; it 
may therefore be increased to a degree that is only lim- 
ited by our inability to restrain it, and is the greatest 
power that has been made subservient to the wants of 
man. 



228 STEAM. SECT. XXV. 

It is found that the absolute quantity of heat consumed 
in the process of converting water into steam is the same 
at whatever temperature water may boil, but that the 
latent heat of steam is always greater exactly in the same 
proportion as its sensible heat is less. Steam raised at 
212 under the ordinary pressure of the atmosphere, 
and steam raised at 180 under half that pressure, con- 
tain the same quantity of heat, with this difference, that 
the one has more latent heat and less sensible heat than 
the other. It is evident that the same quantity of heat 
is requisite for converting a given weight of water into 
steam, at whatever temperature or under whatever 
pressure the water may be boiled ; and therefore in the 
steam engine, equal weights of steam at a high pressure 
and a low pressure are produced by the same quantity 
of fuel ; and whatever the pressure of the steam may 
be, the consumption of fuel is proportional to the quan- 
tity of water converted into vapor. Steam at a high 
pressure expands as soon as it comes into the air, by 
which some of its sensible heat becomes latent ; and as 
it naturally has less sensible heat than steam raised under 
low pressure, its actual temperature is reduced so much 
that the hand may be plunged into it without injury the 
instant it issues from the orifice of a boiler. 

The elasticity or tension of steam, like that of common 
air, varies inversely as its volume ; that is, when the 
space it occupies is doubled, its elastic force is reduced 
one-half. The expansion of steam is indefinite ; the 
smallest quantity of water when reduced to the form of 
vapor, will occupy many millions of cubic feet ; a wonder- 
ful illustration of the minuteness of the ultimate parti- 
cles of matter ! The latent heat absorbed in the forma- 
tion of steam is given out again by its condensation. 

Steam is formed throughout the whole mass of a 
boiling liquid, whereas evaporation takes place only at 
the free surfaces of liquids, and that under the ordinary 
temperature and pressure of the atmosphere. There 
is a constant evaporation from the land and water all 
over the earth. The rapidity of its formation does not 
altogether depend upon the dryness of the air ; according 
to Dr. Dalton's experiments, it depends also on the dif- 
ference between the tension of the vapor which is form- 



S*CT. XXV. APPLICATION OF HEAT. 229 

ing and that which is already in the atmosphere. In 
calm weather, vapor accumulates in the stratum of air 
immediately above the evaporating surface, and retards 
the formation of more ; whereas a strong wind accele- 
rates the process, by carrying off the vapor as soon as 
it rises, and making way for a succeeding portion of 
dry air. 

The latent heat of ah* and all elastic fluids may be 
forced out by sudden compression, like squeezing water 
out of sponge. The quantity of heat brought into action 
in this way is very well illustrated hi the experiment of 
igniting a piece of timber by the sudden compression of 
air by a piston thrust into a cylinder closed at one end : 
the development of heat on a stupendous scale is exhib- 
ited in lightning, probably produced in part by the violent 
compression of the atmosphere during the passage of 
the electric fluid. Prodigious quantities of heat are 
constantly becoming latent, or are disengaged by the 
changes of condition to which substances are liable in 
passing from the solid to the liquid, and from the liquid 
to the gaseous form, or the contrary, occasioning endless 
vicissitudes of temperature over the globe. 

There are many other sources of heat, such as com- 
bustion, friction, and percussion, all of which are only 
means of calling a power into evidence which already 
exists. 

The application of heat to the various branches of the 
mechanical and chemical arts has, within a few years, 
effected a greater change in the condition of man than 
had been accomplished in any equal period of his exist- 
ence. Armed by the expansion and condensation of 
fluids with a power equal to that of the lightning itself, 
conquering time and space, he flies over plains, and trav- 
els on paths cut by human industry even through moun- 
tains, with a velocity and smoothness more like planetary 
than terrestrial motion ; he crosses the deep hi opposi- 
tion to wind and tide ; by releasing the strain on the 
cable, he rides at anchor fearless of the storm ; he makes 
the elements of air and water the carriers of warmth, 
not only to banish winter from his home, but to adorn it 
even during the snow-storm with the blossoms of spring; 
and, like a magician, he raises, from the gloomy and 
U 



230 SIMILARITY OF LIGHT, HEAT, ETC. SECT. XXV. 

deep abyss of the mine, the spirit of light to dispel the 
midnight darkness. 

It has been observed that heat, like light and sound, 
probably consists in the undulations of an elastic medium. 
All the principal phenomena of heat may actually be 
illustrated by a comparison with those of sound. The 
excitation of heat and sound are not only similar but 
often identical, as in friction and percussion ; they are 
both communicated by contact and radiation ; and Dr. 
Young observes, that the effect of radiant heat in raising 
the temperature of a body upon which it falls, resembles 
the sympathetic agitation of a string when the sound of 
another string which is in unison with it is transmitted 
through the air. Light, heat, sound, and the waves of 
fluids, are all subject to the same laws of reflection, and 
indeed their undulatory theories are perfectly similar. 
If, therefore, we may judge from analogy, the undula- 
tions of some of the heat-producing rays must be less 
frequent than those of the extreme red of the solar spec- 
trum ; but the analogy is now perfect, since the inter- 
ference of heat is no longer a matter of doubt : hence 
the interference of two hot rays must produce cold ; 
darkness results from the interference of two undula- 
tions of light ; silence ensues from the interference of 
two undulations of sound ; and still water, or no tide, is 
the consequence of the interference of two tides. The 
propagation of sound, however, requires a much denser 
medium than that either of light or heat ; its intensity 
diminishes as the rarity of the air increases ; so that, at 
a very small height above the surface of the earth, the 
noise of the tempest ceases, and the thunder is heard 
no more in those boundless regions where the heavenly 
bodies accomplish their periods in eternal and sublime 
silence. 

A consciousness of the fallacy of our senses is one of 
the most important consequences of the study of nature. 
This study teaches us that no object is seen by us in its 
true place, owing to aberration ; that the colors of sub- 
stances are solely the effects of the action of matter upon 
light ; and that light itself, as well as heat and sound, are 
not real beings, but mere modes of action communicated 
to our perceptions by the nerves. The human frame 



Sccr. XXV. HERSCHEI/S EXPERIMENTS. 231 

may therefore be regarded as an elastic system, the dif- 
ferent parts of which are capable of receiving the tremors 
of elastic media, and of vibrating in unison with any num- 
ber of superposed undulations, all of which have their 
perfect and independent effect. Here our knowledge 
ends ; the mysterious influence of matter on mind will 
in all probability be forever hid from man. 

A series of experiments by Sir John Herschel has 
disclosed a new set of obscure rays hi the solar spec- 
trum, which seem to bear the same relation to those of 
heat that the photographic or chemical rays bear to the 
luminous. They are situate in that part of the spec- 
trum which is occupied by the less refrangible visible 
colors, and have been named by their discoverer Parather- 
mic rays. It must be held in remembrance that the 
region of greatest heat in the solar spectrum lies in the 
dark space beyond the visible red. Now Sir John Her- 
schel found that in experiments with a solution of gum 
guaiacum in soda, which gives the paper a green color, 
the green, yellow, orange, and red rays of the spectrum 
invariably discharged the color, while no effect was pro- 
duced by the extra-spectral rays of caloric, which ought 
to have had the greatest effect, had heat been the cause 
of the phenomenon. When an aqueous solution of 
chlorine was poured over a slip of paper prepared with 
gum guaiacum dissolved in soda, a color varying from a 
deep somewhat greenish hue to a fine celestial blue was 
given to it ; and when the solar spectrum was thrown 
on the paper while moist, the color was discharged from 
all the space under the less refrangible luminous rays, 
at the same time that the more distant thermic rays 
beyond the spectrum evaporated the moisture from the 
space on which they fell : so that the heat spots became 
apparent. But the spots disappeared as the paper 
dried, leaving the surface unchanged ; while the photo- 
graphic impression within the visible spectrum increased 
in intensity, the non-luminous thermic rays, though 
evidently active as to heat, were yet incapable of effect- 
ing that peculiar chemical change which other rays of 
much less heating power were all the time producing. 
Sir John having ascertained that an artificial heat from 
180 to 280 of Fahrenheit changed the green tint of 



232 EXPERIMENTS ON LIGHT AND HEAT. SECT. XXV. 

gum guaiacum to its original yellow hue when moist, 
but that it had no such effect when dry, he therefore 
tried whether heat from a hot iron applied to the back 
of the paper used in the last-mentioned experiment 
while under the influence of the solar spectrum might 
not assist the action of the calorific rays ; but instead of 
doing so, it greatly accelerated the discoloration over the 
spaces occupied by the less refrangible rays, but had no 
effect on the extra-spectral region of maximum heat. 
Obscure terrestrial heat therefore is capable of assisting 
and being assisted in effecting this peculiar change by 
those rays of the spectrum, whether luminous or ther- 
mic, which occupy its red, yellow, and green regions, 
while on the other hand it receives no such assistance 
from the purely thermic rays beyond the spectrum 
acting under similar circumstances and in an equal state 
of condensation. 

The conclusions drawn from these experiments are 
confirmed by that which follows : a photographic picture 
formed on paper prepared with a mixture of the solu- 
tions of ammonia-citrate of iron and ferro-sesquicyanite 
of potash in equal parts, then thrown into water and 
afterward dried, will be blue and negative, that is to 
say, the lights and shadows will be the reverse of what 
they are in nature. If in this state the paper be washed 
with a solution of proto-nitrate of mercury, the picture 
will be discharged : but if it be well washed and dried 
and a hot smoothing iron passed over it, the picture in- 
stantly reappears, not blue, but brown: if kept some 
weeks in this state in perfect darkness between the 
leaves of a portfolio, it fades and almost entirely vanishes, 
but a fresh application of heat restores it to its full origi- 
nal intensity. This curious change is not the effect of 
light, at least not of light alone. A certain temperature 
must be attained, and that suffices in total darkness : yet 
on exposing to a very concentrated spectrum a slip of the 
paper used in the last experiment, after the uniform 
blue color has been discharged and a white ground left, 
this whiteness is changed to brown over the whole re- 
gion of the red and orange rays, but not beyond the 
luminous spectrum. 

Sir John thence concludes 1st. That it is the heat 



SKCT. XXV. CONCLUSIONS TO BE DRAWN. 233 

of these rays, not their light, which operates the 
change ; 2dly. That this heat possesses a peculiar 
chemical quality which is not possessed by the purely 
calorific rays outside of the visible spectrum, though far 
more intense ; and, 3dly. That the heat radiated from 
obscurely hot iron, abounds especially in rays analogous 
to those of the region of the spectrum above indicated. 

Another instance of these singular transformations 
may be noticed. The pictures formed on cyanotype 
paper, rendered more sensitive by the addition of cor- 
rosive sublimate, are blue on a white ground and posi- 
tive, that is, the lights and shadows are the same as in 
nature, but by the application of heat, the color is 
changed from blue to brown, from positive to negative ; 
even by keeping in darkness the blue color is restored, 
as well as the positive character. Sir John attributes 
this as in the former instance to certain rays, which re- 
garded as rays of heat or light, or of some influence sui 
generis accompanying the red and orange rays of the 
spectrum, are also copiously emitted by bodies heated 
short of redness. He thinks it probable that these in- 
visible parathermic rays are the rays which radiate 
from molecule to molecule in the interior of bodies, that 
they determine the discharge of vegetable colors at the 
boiling temperature, and also the innumerable atomic 
transformations of organic bodies which take place at 
the temperature below redness, that they are distinct 
from' those of pure heat, and that they are sufficiently 
identified by these characters to become legitimate ob- 
jects of scientific discussion. 

The calorific and parathermic rays appear to be so 
intimately connected with the discoveries of Messrs. 
Draper and Moser that the subject of solar radiation 
would be imperfect were they omitted. The dis- 
covery of Daguerre shows that the action of light on 
the iodide of silver renders it capable of condensing the 
vapor of mercury which adheres to the parts affected 
by it. Professor Moser of KOnigsberg has proved that 
the same effect is produced by the simple contact of 
bodies, and even by their very near juxta-position, and 
that in total darkness as well as in light. This dis- 
covery he announced in the following words : " If a 
u2 



234 DISCOVERIES OF PROFESSOR MOSER. SECT. XXV. 

surface has been touched in any particular parts by any 
body, it acquires the property of precipitating all va- 
pors, and these adhere to it or combine chemically with 
it on those spots differently to what they do on the un- 
touched parts." If we write on a plate of glass or any 
smooth surface whatever with blotting paper, a brush, 
or anything else, and then clean it, the characters al- 
ways reappear if the plate or surface be breathed upon, 
and the same effect may be produced even on the sur- 
face of mercury ; nor is absolute contact necessary. If 
a screen cut in a pattern be held over a polished me- 
tallic surface at a small distance, and the whole breathed 
on : after the vapor has evaporated so that no trace is 
left on the surface, the pattern comes out when it is 
breathed on again. 

Professor Moser proved that bodies exert a very de- 
cided influence upon each other, by placing coins, cut 
stones, pieces of horn, and other substances, a short 
time on a warm metallic plate ; when the substance 
was removed no impression appeared on the plate till it 
was breathed upon or exposed to the vapor of mercury, 
and then these vapors adhered only to the parts where 
the substance had been placed, making distinct images, 
which in some cases were permanent after the vapor 
was removed. Similar impressions were obtained on 
glass and other substances even when the bodies were 
not in contact, and the results were the same whether 
the experiments were performed in light or in darkness. 

Mr. Hunt has shown that many of these phenomena 
depend on difference of temperature, and that in order 
to obtain good impressions dissimilar metals must be 
used. For example, gold, silver, bronze, and copper 
coins were placed on a plate of copper too hot to be 
touched, and allowed to remain till the plate cooled ; 
all the coins had made an impression, the distinctness 
and intensity of which was in the order of the metals 
named. When the plate was exposed to the vapor of 
mercury the result was the same, but when the vapor 
was wiped off, the gold and silver coins only had left 
permanent images on the copper. These impressions 
are often minutely perfect whether the coins are in 
actual contact with the plate or of an inch above it. 



SECT. XXV. LATENT CALORIC. 235 

The mass of the metal has a material influence on the 
result ; a large copper coin makes a better impression 
on a copper plate than a small silver coin. When coins 
of different metals are placed on the same -plate they 
interfere with each other. 

When, instead of being heated, the copper plate 
was cooled by a freezing mixture, and bad conductors of 
heat laid upon it, as wood, paper, glass, &c., the result 
was similar, showing that the phenomena could be pro- 
duced by any disturbance of the caloric latent in the 
substances. 

There can be no doubt that these phenomena are 
universal, since all substances are more or less sensitive 
to light, which must produce innumerable changes in 
the nature of terrestrial things, especially in the vege- 
table tribe, by the power it gives of condensing vapor 
and consequently the deposition of dew. 

Red and orange-colored media, smoked glass, and all 
bodies that transmit or absorb the calorific rays freely, 
leave strong impressions on a plate ef copper whether 
they be in contact or | of an inch above the plate. The 
strongest proof that heat is concerned in some at least 
of these phenomena is evident. For instance, a solar 
spectrum concentrated by a lens was thrown on a pol- 
ished plate of copper and kept on the same spot by a 
heliostat for one, two, or three hours ; when exposed 
to mercurial vapor a film of the vapor covered the plate 
where the diffused light which always accompanies the 
solar spectrum had fallen ; on the obscure space occu- 
pied by the maximum heating power of Sir William 
Herschel, and also the great heat spot in the thermic 
spectrum of Sir John Herschel, the condensation of the 
mercury was so thick that it stood out a distinct white 
spot on the plate, while over the whole space that had 
been under the visible spectrum the quantity of vapor 
was much less than that which covered the other parts, 
affording distinct evidence of a negative effect hi the 
luminous spectrum, and of the power of the calorific 
rays, which is not always confined to the surface of the 
metal, since in many instances the impressions are formed 
to a considerable depth below it, and consequently are 
permanent. 



236 THE ART OP THERMOGRAPHY. SECT. XXV. 

Mr. Hunt observing that a black substance leaves a 
stronger impression on a metallic surface than a white, 
applied the property to the art of thermography, by 
which he copies prints, wood-cuts, writing, and printing, 
on copper amalgamated on one surface and highly pol- 
ished, merely by placing the object to be copied 
smoothly on the metal and pressing it into close contact 
by a plate of glass : after some hours the plate is sub- 
j ected to the vapor of mercury and afterward t6 that of 
iodine, when a black and accurate impression of the 
object comes out on a gray ground. Effects similar to 
those attributed to heat may also be produced by elec- 
tricity : Mr. Karsten, by placing a glass plate upon one 
of metal, and on the glass plate a medal subjected to 
discharges of electricity, found a perfect image of the 
medal impressed on the glass, which could be brought 
into evidence by either mercury or iodine ; and when 
several plates of glass were interposed between the 
medal and the metallic plate, each plate of glass re- 
ceived an image on its upper surface after the passage 
of electrical discharges. These discharges have the 
remarkable power of restoring impressions that have 
been long obliterated from plates by polishing ; a proof 
that the disturbances upon which these phenomena 
depend are not confined to the surface of the metals, 
but that a very decided molecular change has taken 
place to a considerable depth. Mr. Hunt's experiments 
prove that the electro-negative metals make the most 
decided images upon electro-negative plates, and vice 
versa. M. Matteucci has shown that a discharge of 
electricity does not visibly affect a polished silver plate, 
but that it produces an alteration which renders it capa- 
ble of condensing vapor. 

M. Fizean ascribes a numerous class of these phe- 
nomena to the action of a slight layer of organic or fatty 
matter on the surfaces, which, being volatile, is trans- 
ferred to any body near, in a greater or less quantity ac- 
cording to the distance ; that is, according as the sur- 
face projects or sinks into hollows. When the different 
parts of a surface are unequally soiled by extraneous 
bodies, even in the minutest quantity, the condensation 
of mercurial vapor is effected in a manner visibly dif- 



SECT. XXV. VARIOUS PHENOMENA EXPLAINED. 237 

ferent on its different parts, and therefore images are 
formed. Although this explains various phenomena, it 
does not apply to those already described, as Mr. Hunt 
had taken the precaution to divest the substances he 
used of every trace of organic matter. 

It is difficult to see to what cause Mr. Hunt's experi- 
ments on the reciprocal action of bodies in total darkness 
can be attributed, unless perhaps to a constant radiation 
of some peculiar principle from their surfaces, which 
really seems to exist. 

The impression of an engraving was made by laying 
it face downwards on a silver plate iodized, and placing 
an amalgamated copper plate upon it : it was left hi 
darkness fifteen hours, when an impression of the en- 
graving had been made on the amalgamated plate, 
through the paper. 

As the same may be obtained on plates of iron, zinc, 
or lead, it is evident that this result is not the effect of 
chemical rays. 

An iodized silver plate was placed in darkness with a 
coil of string laid on it, and with a polished silver plate 
suspended one eighth of an inch above it ; after four 
hours they were exposed to the vapors of mercury, 
which became uniformly deposited on the iodized plate, 
but on the silver one there Was a sharp image of the 
string, so that this image was formed in the dark, and 
even without contact. Coins or other objects leave 
their impressions in the same manner with perfect 
sharpness and accuracy, when brought out by vapor 
without contact, in darkness, and on simple metals. 

Heat, electricity, and the evaporation of unctuous 
matter, may account for some of these phenomena, but 
Qthers clearly point at some unknown influence exerted 
between the surfaces of solid bodies, and affecting their 
molecular structure so as to determine the precipitation 
of vapors, an influence which in all probability will ulti- 
mately be found to be either the parathermic rays of 
Sir John Herschel, or ultimately connected with them. 



238 ATMOSPHERE OF THE MOON. JECT. XXVL 



SECTION XXVI. 

Atmosphere of the Planets and the Moon Constitution of the Sun Esti- 
mation of the Sun's tight His Influence on the different Planets 
Temperature of Space Internal Heat of the Earth Zone of Constant 
Temperature Heat increases with the Depth Heat in Mines and 
Wells Thermal Springs Central Heat Volcanic Action The Heat 
above the Zone of Constant Temperature entirely from the Sun The 
Quantity of Heat annually received from the Sun Isogeothermal Lines 
Distribution of Heat on the Earth Climate Line of Perpetual Con- 
gelation Causes affecting Climate Isothermal Lines Excessive Cli- 
mates The same Quantity of Heat annually received and radiated by 
the Earth. 

THE ocean of light and heat perpetually flowing from 
the sun, must affect the bodies of the system very differ- 
ently, on account of the varieties in their atmospheres, 
some of which appear to be very extensive and dense. 
According to the observations of Schroeter, the atmos- 
phere of Ceres is more than 668 miles high, and that of 
Pallas has an elevation of 465 miles. These must re- 
fract the light and prevent the radiation of heat like our 
own. But it is remarkable that not a trace of atmosphere 
can be perceived in Vesta. The action of the sun's rays 
must be very different on such bodies from what it is 
on the earth, and the heat imparted to them quickly 
lost by radiation ; yet it is impossible to estimate their 
temperature, since the cold may be counteracted by 
their central heat, if, as there is reason to presume, they 
have originally been in a state of fusion, possibly of 
vapor. The attraction of the earth has probably de- 
prived the moon of hers ; for the refractive power of 
the air at the surface of the earth is at least a thousand 
times as great as refraction at the surface of the moon. 
The lunar atmosphere, therefore, must be of a greater 
degree of rarity than can be produced by our best air- 
pumps ; consequently no terrestrial animal could exist 
in it. This was confirmed by M. Arago's observations 
during the last great solar eclipse, when no trace of a 
lunar atmosphere was to be seen. 

The sun has a very dense atmosphere, which is 
probably the cause of the peculiar phenomena in his 
photographic image already mentioned. What his body 
may be, it is impossible to conjecture ; but he seems to 



SECT. XXVI. CONSTITUTION OF THE SUN. 239 

be surrounded by a mottled ocean of flame, through 
which his dark nucleus appears like black spots often of 
enormous size. These spots are almost always com- 
prised within a zone of the sun's surface, whose breadth, 
measured on a solar meridian, does not extend beyond 30$ 
on each side of his equator, though they have been seen 
at the distance of 39i. From their extensive and rapid 
changes, there is every reason to suppose that the exte- 
rior and incandescent part of the sun is gaseous. The 
solar rays, probably arising from chemical processes that 
continually take place at his surface, or from electricity, 
are transmitted through space in all directions ; but not- 
withstanding the sun's magnitude, and the inconceivable 
heat that must exist at his surface, as the intensity both 
of his light and heat diminishes as the square of the dis- 
tance increases, his kindly influence can hardly be felt 
at the boundaries of our system, or at all events it must 
be but feeble. 

The direct light of the sun has been estimated to be 
equal to that of 5563 wax candles of moderate size, sup- 
posed to be placed at the distance of one foot from the 
object. That of the moon is probably only equal to the 
light of one candle at the distance of twelve feet. Con- 
sequently the light of the sun is more than three hundred 
thousand times greater than that of the moon. Hence 
the light of the moon imparts no heat. Professor Forbes 
is convinced by recent experiments that the direct light 
of the moon is incapable of raising a thermometer one 
three-hundred-thousandth part of a centigrade degree, 
at least in this climate. The intensity of the sun's light 
diminishes from the center to the circumference of the 
solar disc. 

In Uranus, the sun must be seen like a small but bril- 
liant star, not above the hundred and fiftieth part so 
bright as he appears to us ; but that is 2000 times brighter 
than our moon ; so that he is really a sun to Uranus, 
and may impart some degree of warmth. But if we 
consider that water would not remain fluid in any part 
of Mars, even at his equator, and that in the temperate 
zones of the same planet even alcohol and quicksilver 
would freeze, we may form some idea of the cold that 
must reign in Uranus. 



240 TEMPERATURE OF SPACE. SECT. XXVI. 

The climate of Venus more nearly resembles that of 
the earth, though, excepting perhaps at her poles, much 
too hot for animal and vegetable life as they exist here ; 
but in Mercury, the mean heat arising only from the 
intensity of the sun's rays must be above that of boiling 
quicksilver, and water would boil even at his poles. 
Thus the planets, though kindred with the earth in mo- 
tion and structure, are totally unfit for the habitation of 
such a being as man, unless, indeed, their temperature 
should be modified by circumstances of which we are 
not aware, and which may increase or diminish the 
sensible heat so as to render them habitable. 

It is found by experience, that heat is developed in 
opaque and translucent substances by their absorption of 
solar light, but that the sun's rays do not sensibly alter 
the temperature of perfectly transparent bodies through 
which they pass. As the temperature of the pellucid 
planetary space can be but little affected by the passage 
of the sun's light and heat, neither can it be sensibly 
raised by die heat now radiated from the earth ; conse- 
quently its temperature must be invariable, at least 
throughout the extent of the solar system. The at- 
mosphere, on the contrary, gradually increasing in den- 
sity toward the surface of the earth, becomes less pel- 
lucid, and therefore gradually increases in temperature, 
both from the direct action of the sun, and from the ra- 
diation of the earth. Lambert had proved that the ca- 
pacity of the atmosphere for heat varies according to the 
same law with its capacity for absorbing a ray of light 
passing through it from the zenith, whence M. Svanberg 
found that the temperature of space is 58 below the 
zero point of Fahrenheit's thermometer. From other 
researches, founded upon the rate and quantity of at- 
mospheric refraction, he obtained a result which only 
differs from the preceding by half a degree. M. Fourier 
has arrived at nearly the same conclusion from the law 
of the radiation of the heat of the terrestrial spheroid, 
on the hypothesis of its having nearly attained its limit 
of temperature in cooling down from its supposed prim- 
itive state of fusion. The difference in the result of 
these three methods, totally independent of one another, 
only amounts to the fraction of a degree. 



SKOT. XXVI. INTERNAL HEAT OF THE EARTH. 241 

The cold endured by Sir Edward Parry one day in 
Melville Island was 55 below zero ; and that suffered 
by Captain Back on the 17th of January, 1834, in 62 
46^' of north latitude, was no less than 70 below the 
same point. However, M. Poisson attributes this to ac- 
cidental circumstances, and by a recent computation, he 
makes the temperature of space to be 8 above the zero 
of Fahrenheit. This he considers greatly to exceed the 
temperature of the exterior strata of the atmosphere, 
which he conceives to be deprived of their elasticity by 
intense cold, and he thus accounts for the decrease of 
temperature at great elevations, and for the limited ex- 
tent of the atmosphere. 

Doubtless, the radiation of all the bodies in the uni- 
verse maintains the ethereal medium at a higher tem- 
perature than it would otherwise have, and must event- 
ually increase it, but by a quantity so evanescent that it 
is hardly possible to conceive a time when a change will 
become perceptible. 

The temperature of space being so low, it becomes a 
matter of no small interest to ascertain whether the earth 
may not be ultimately reduced by radiation to the tem- 
perature of the surrounding medium ; what the sources 
of heat are ; and whether they be sufficient to compen- 
sate the loss, and to maintain the earth in a state fit for 
the support of animal and vegetable life in time to come. 
All observations that have been made under the surface 
of the ground concur in proving that there is a stratum 
at the depth of from 40 to 100 feet throughout the whole 
earth, where the temperature is invariable at all times 
and seasons, and which differs but little from the mean 
annual temperature of the country above. According to 
M. Boussingault, indeed, that stratum at the equator is 
at the depth of little more than a foot in places sheltered 
from the direct rays of the sun ; but in our climates it 
is at a much greater depth. In the course of more than 
half a century, the temperature of the earth at the 
depth of 90 feet in the caves of the Observatory at Paris 
has never been above or below 53 of Fahrenheit's ther- 
mometer, which is only 2 above the mean annual tem- 
perature at Paris. This zone, unaffected by the sun's 
rays from above, or by the internal heat from below, 
16 X 



242 HEAT IN MINES AND WELLS. SECT. XXVI. 

serves as an origin whence the effects of the external 
heat are estimated on one side, and the internal temper- 
ature of the globe on the other. 

As early as the year 1740, M. Gensanne discovered 
in the lead mines of Geromagny, three leagues from 
Befort, that the heat of the ground increases with the 
depth below the zone of constant temperature. A vast 
number of observations have been made since that time 
in the mines of Europe and America, by MM. Saussure, 
Daubuisson, Humboldt, Cordier, Fox, Reich, and others, 
which agree, without an exception, in proving that the 
temperature of the earth becomes higher in descending 
toward its center. The greatest depth that has been 
attained is in the silver mine of Guamaxato in Mexico, 
where M. de Humboldt found a temperature of 98 at 
the depth of 285 fathoms ; the mean annual temperature 
of the country being only 61. Next to that is the Dal- 
coath copper mine in Cornwall, where Mr. Fox's ther- 
mometer stood at 68 in a hole in the rock at the depth 
of 230 fathoms, and at 82 in water at the depth of 240 
fathoms, the mean annual temperature at the surface 
being about 50. But it is needless to multiply exam- 
ples, all of which concur in showing that there is a very 
great difference between the temperature in the interior 
of the earth and at its surface. Mr. Fox's observations 
on the temperature of springs which rise at profound 
depths in mines, afford the strongest testimony. He 
found considerable streams flowing into some of the 
Cornish mines at the temperature of 80 or 90, which 
is about 30 or 40 above that of the surface; and also 
ascertained that nearly 2,000,000 gallons of water are 
daily pumped from the bottom of the Poldice mine, 
which is 176 fathoms deep, at 90 or 100. As this is 
higher than the warmth of the human body, Mr. Fox 
justly observes that it amounts to a proof that the in- 
creased temperature cannot proceed from the persons of 
the workmen employed in the mines. Neither can the 
warmth of mines be attributed to the condensation of 
the currents of air which ventilate them. Mr. Fox, 
whose opinion is of high authority in these matters, 
states that even in the deepest mines, the condensation 
of the air would not raise the temperature more than 



. XXVI. HEAT IN MINES AND WELLS. 243 

5 or 6, and that if the heat could be attributed to this 
cause, the seasons would sensibly affect the temperature 
of mines, which it appears they do not where the deptk 
is great. Besides, the Cornish mines are generally 
ventilated by numerous shafts opening into the galleries 
from the surface or from a higher level. The air circu- 
lates freely in these, descending in some shafts and as- 
cending in others. In all cases, Mr. Fox found that the 
upward currents are of a higher temperature than the 
descending currents ; so much so, that in winter the 
moisture is often frozen in the latter to a considerable 
depth ; the circulation of air, therefore, tends to cool 
the mine instead of increasing the heat. Mr. Fox has 
also removed the objections arising from the compara- 
tively low temperature of the water in the shafts of 
abandoned mines, by showing that observations in them, 
from a variety of circumstances which he enumerates, 
are too discordant to furnish any conclusion as to the 
actual heat of the earth. The high temperature of 
mines might be attributed to the effects of the fires, 
candles, and gunpowder used by the miners, did not a 
similar increase obtain in deep wells, and in borings to 
great depths in search of water, where no such causes 
of disturbance occur. In a well dug with a view to 
discover salt in the canton of Berne, and long deserted, 
M. de Saussure had the most complete evidence of in- 
creasing heat. The same has been confirmed by the 
temperature of many wells, both in France and England, 
especially by the Artesian wells, so named from a pecu- 
liar method of raising water first resorted to in Artois, 
and since become very general. An Artesian well con- 
sists of a shaft of a few inches in diameter, bored into 
the earth till a spring is found. To prevent the water 
being earned off by the adjacent strata, a tube is let 
down which exactly fills the bore from top to bottom, in 
which the water rises pure to the surface. It is clear 
the water could not rise unless it had previously de- 
scended from high ground through the interior of the 
earth to the bottom of the well. It partakes of the 
temperature of the strata through which it passes, and 
in every instance has been warmer in proportion to the 
depth of the well ; but it is evident that the law of in- 



244 THERMAL SPRINGS. SKCT. XXVI. 

crease cannot be obtained in this manner. Perhaps the 
most satisfactory experiments on record are those made 
by MM. August de la Rive and F. Marcet during the 
year 1833, in a boring for water about a league from 
Geneva, at a place 318 feet above the level of the lake. 
The depth of the bore was 727 feet, and the diameter 
only between four and five inches. No spring was ever 
found ; but the shaft filled with mud, from the moisture 
of the ground mixing with the earth displaced in boring, 
which was peculiarly favorable for the experiments, as 
the temperature at each depth may be considered to be 
that of the particular stratum. In this case, where none 
of the ordinary causes of disturbance could exist, and 
where every precaution was employed by scientific and 
experienced observers, the temperature was found to 
increase regularly and uniformly with the depth at the 
rate of about 1 of Fahrenheit for every 52 feet. Pro- 
fessor Reich of Freyberg has found that the mean of a 
great number of observations both in mines and wells is 
1 of Fahrenheit for every 55 feet of depth, and from 
M. Arago's observations in an Artesian well now boring 
in Paris, the increase is 1 of Fahrenheit for every 45 
feet. Though there can be no doubt as to the increase 
of temperature in penetrating the crust of the earth, 
there is still much uncertainty as to the law of increase, 
which varies with the nature of the soil and other local 
circumstances ; but on an average, it has been estimated 
at the rate of 1 for eveiy 50 or 60 feet, which corre- 
sponds with the observations of MM. Marcet and de la 
Rive. In consequence of the rapid increase of internal 
heat, thermal springs, or such as are independent of 
volcanic action, rising from a great depth, must neces- 
sarily be very rare and of a high temperature, and it is 
actually found that none are so low as 68 of Fahren- 
heit : that of Chaudes Aigues in Auvergne is about 
136. In many places warm water from Artesian wells 
will probably come into use for domestic purposes, and 
it is even now employed in manufactories at Wurtem- 
berg, in Alsace, and near Stutgardt. 

It is hardly to be expected that at present any infor- 
mation with regard to the actual internal temperature 
of the earth should be obtained from that of the ocean, 



SECT. XXVI. CENTRAL HEAT OP THE EARTH. 245 

on account of the mobility of fluids, by which the colder 
masses sink downward, while those that are warmer 
rise to the surface. Nevertheless it may be stated, that 
the temperature of the sea decreases with the depth 
between the tropics ; while on the contrary, all our 
northern navigators found that the temperature increases 
with the depth in the polar seas. The change takes 
place about the 70th parallel of latitude. Some ages 
hence, however, it may be known whether the earth 
has arrived at a permanent state as to heat, by comparing 
secular observations of the temperature of the ocean if 
made at a great distance from the land. 

Should the earth's temperature increase at the rate 
of 1 for every fifty feet, it is clear that at the depth of 
200 miles the hardest substances must be in a state of 
fusion, and our globe must in that case either be encom- 
passed by a stratum of melted lava at that depth, or it 
must be a ball of liquid fire 7600 miles in diameter, in- 
closed in a thin coating of solid matter ; for 200 miles 
are nothing when compared with the size of the earth. 
No doubt the form of the earth, as determined by the 
pendulum and arcs of the meridian, as well as by the 
motions of the moon, indicates original fluidity and subse- 
quent consolidation and reduction of temperature by ra- 
diation ; but whether the law of increasing temperature 
is uniform at still greater depths than those already 
attained by man, it is impossible to say. At all events, 
internal fluidity is not inconsistent with the present 
state of the earth's surface, since earthy matter is as 
bad a conductor of caloric as lava, which often retains 
its heat at a very little depth for years after its surface 
is cool. Whatever the radiation of the earth might 
have been in former times, certain it is that it goes on 
very slowly in our days ; for M. Fourier has computed 
that the central heat is decreasing from radiation by 
only about the j^^th part of a second in a century. If 
so, there can be no doubt that it will ultimately be dis- 
sipated ; but as far as regards animal and vegetable life, 
it is of very little consequence whether the center of 
our planet be liquid fire or ice, since its condition in 
either case could have no sensible effect on the climate at 
its surface. The internal fire does not even impart heat 
x2 



246 VOLCANIC ACTION. SECT. XXVI. 

enough to melt the snow at the poles, though so much 
nearer to the center than any other part of the globe. 

The immense extent of active volcanic fire is one of 
the causes of heat which must not be overlooked. 

The range of the Andes from Chili to the north of 
Mexico, probably from Cape Horn to California, or even 
to New Madrid in the United States, is one vast district 
of igneous action, including the Caribbean Sea and the 
West Indian Islands on one hand ; and stretching quite 
across the Pacific Ocean, through the Polynesian Archi- 
pelago, the New Hebrides, the Georgian and Friendly 
Islands, on the other. Another chain begins with the 
Aleutian Islands, extends to Kamtschatka, and from 
thence passes through the Kurile, Japanese, and Phil- 
ippine Islands, to the Moluccas, whence it spreads with 
terrific violence through the Indian Archipelago, even 
to the Bay of Bengal. Volcanic action may again be 
followed from the entrance of the Persian Gulf to Mad- 
agascar, Bourbon, the Canaries, and Azores. Thence 
a continuous igneous region extends through about 1000 
geographical miles to the Caspian Sea, including the 
Mediterranean, and extending north and south between 
the 35th and 40th parallels of latitude ; and in central 
Asia a volcanic region occupies 2500 square geographical 
miles. The volcanic fires are developed in Iceland in 
tremendous force ; and the antarctic land recently dis- 
covered by Sir James Ross is an igneous formation of 
the boldest structure, from whence a volcano in high 
activity rises 12,000 feet above the perpetual ice of 
these polar deserts, and within 19 of the south pole. 
Throughout this vast portion of the world the subterra- 
neous fire is often intensely active, producing such vio- 
lent earthquakes and eruptions that their effects, accu- 
mulated during millions of years, may account for many 
of the great geological changes of igneous origin that 
have already taken place in the earth, and may occasion 
others not less remarkable, should time that essential 
element in the vicissitudes of the globe be granted, and 
their energy last. 

Mr. Lyell, who has shown the power of existing causes 
with great ingenuity, estimates that on an average twenty 
eruptions take place annually in different parts of tho 



SECT. XX VI. VOLCANIC ERUPTTONS. 247 

world ; and many must occur or have happened, even on 
the most extensive and awful scale, among people equally 
incapable of estimating their effects and of recording 
them. We should never have known the extent of the 
fearful eruption which took place in the island of Sum- 
bawa, in 1815, but for the accident of Sir Stamford Raf- 
fles having been governor of Java at the time. It began 
on the 5th of April, and did not entirely cease till July. 
The ground was shaken through an area of 1000 miles 
in circumference ; the tremors were felt in Java, the 
Moluccas, a great part of Celebes, Sumatra, and Borneo. 
The detonations were heard in Sumatra, at the distance 
of 970 geographical miles in a straight line ; and at Ter- 
nate, 720 miles in the opposite direction. The most 
dreadful whirlwinds carried men and cattle into the ah* ; 
and with the exception of 26 persons, the whole popu- 
lation of the island perished to the amount of 12,000. 
Ashes were carried 300 miles to Java, in such quantities 
that the. darkness during the day was more profound 
than ever had been witnessed in the most obscure night. 
The face of the country was changed by the streams of 
lava, and by the upheaving and sinking of the soil. The 
town of Tomboro was submerged, and water stood to 
the depth of 18 feet in places which had been dry land. 
Ships grounded where they had previously anchored, 
and others could hardly penetrate the mass of cinders 
which floated on the surface of the sea for several miles 
to the depth of two feet. A catastrophe similar to this, 
though of less magnitude, took place in the island of Bali 
in 1808, which was not heard of in Europe till years 
afterward. The eruption of Coseguina in the Bay of 
Fonseca, which began on the 19th of January, 1835, and 
lasted many days, was even more dreadful and extensive 
in its effects than that of Sumbawa. The ashes during 
this eruption were carried by the upper current of the 
atmosphere as far north as Chiassa, which is upward 
of 400 leagues to the windward of that volcano. Many 
volcanos supposed to be extinct have all at once burst 
out with inconceivable violence. Witness Vesuvius, on 
historical record ; and the volcano in the island of St. 
Vincent in our own days, whose crater was lined with 
large trees, and which had not been active in the mem- 



248 EARTHQUAKES. SECT. XXVI. 

ory of man. Vast tracts are of volcanic origin where 
volcanos have ceased to exist for ages. Whence it may 
be inferred that in some places the subterraneous fires 
are in the highest state of activity, in some they are 
inert, and in others they appear to be extinct. Yet there 
are few countries that are not subject to earthquakes of 
greater or less intensity ; the tremors are propagated 
like a sonorous undulation to such distances that it is 
impossible to say in what point they originate. In some 
recent instances their power must have been tremendous. 
In South America, so lately as 1822, an area of 100,000 
square miles, which is equal in extent to the half of 
France, was raised several feet above its present level ; 
a most able account of which is given in the ' Transac- 
tions of the Geological Society,' by an esteemed friend 
of the author, Mrs. Graham, now Mrs. Calcott, who 
was present during the whole time of that formidable 
earthquake, which recurred at short intervals for more 
than two months, and who possesses talents to appre- 
ciate, and had opportunities of observing, its effects 
under the most favorable circumstances at Valparaiso, 
and for miles along the coast where it was most intense. 
A considerable elevation of the land has again taken 
place along the coast of Chili, in consequence of the 
violent earthquake which happened on the 20th of Feb- 
ruary, 1835. In 1819, a ridge of land stretching for 50 
miles across the delta of the Indus, 16 feet broad, was 
raised 10 feet above the plain; yet the account of this 
marvelous event was recently brought to Europe by 
Mr. Burnes. The reader is referred to Mr. L yell's 
very excellent work on geology, already mentioned, for 
most interesting details of the phenomena and extensive 
effects of volcanos and earthquakes, too numerous to 
find a place here. It may however be mentioned, that 
innumerable earthquakes are from time to time shaking 
the solid crust of the globe, and carrying destruction to 
distant regions, progressively though slowly accomplish- 
ing the great work of change. These terrible engines 
of ruin, fitful and uncertain as they may seem, must, 
like all durable phenomena, have a law, which may in 
time be discovered by long-continued and accurate ob- 
servations. 



SKCT. XXVI. VOLCANIC THEORIES. 249 

The shell of volcanic fire that girds the globe at a 
small depth below our feet has been attributed to differ- 
ent causes. By some it is supposed to originate in an 
ocean of incandescent matter, still existing in the cen- 
tral abyss of the earth. Some conceive it to be super- 
ficial, and due to chemical action, in strata at no very 
great depth when compared with the size of the globe. 
The more so, as matter on a most extensive scale is 
passing from old into new combinations, which, if rapidly 
effected, are capable of producing the most intense heat. 
According to others, electricity, which is so universally 
diffused in all its forms throughout the earth, if not the 
immediate cause of the volcanic phenomena, at least 
determines the chemical affinities that produce them. 
It is clear that a subject so involved in mystery must 
give rise to much speculation, in which every hypothe- 
sis is attended with difficulties that observation alone 
can remove. 

But the views of Mr. Babbage and Sir John Herschel 
on the general cause of volcanic action, and the changes 
in the equilibrium of the internal heat of the globe, ac- 
cord more with the laws of mechanics and radiant caloric 
than any that have been proposed. The theory of these 
distinguished philosophers, formed independently of each 
other, is equally consistent with observed phenomena, 
whether the earth be a solid crust encompassing a nu- 
cleus of liquid lava, or that there is merely a vast reser- 
voir or stratum of melted matter at a moderate depth 
below the superficial crust. The author is indebted to 
the kindness of Mr. Lyell for the perusal of a most 
interesting letter from Sir John Herschel, in which he 
states his views on the subject. 

Supposing that the globe is merely a solid crust, rest- 
ing upon fluid or semi-fluid matter, whether extending 
to the center or not, the transfer of pressure from one 
part of its surface to another by the degradation of ex- 
isting continents, and the formation of new ones, would 
be sufficient to subvert the equilibrium of heat in the 
interior, and occasion volcanic eruptions. For, since 
the internal heat of the earth is transmitted outwards 
by radiation, an accession of new matter on any part of 
the surface, like an addition of clothing, by keeping it in, 



250 VOLCANIC THEORIES. SECT. XXVI. 

would raise the temperature of the strata below, and in 
the course of ages would even reduce those at a great 
depth to a state of fusion. Some of the substances might 
be converted into gases ; and should the accumulation of 
new matter take place at the bottom of the sea, as is 
generally the case, this lava would be mixed with water 
in a state of ignition in consequence of the enormous 
pressure of the ocean, and of the newly superimposed 
matter which would prevent it from expanding into 
steam. Now Mr. Lyell has shown with his usual talent, 
that the quantity of matter carried down by rivers from 
the surface of the continents is comparatively trifling, 
and that the great transfer to the bottom of the ocean is 
produced at the coast line by the action of the sea ; 
hence, says Sir John Herschel, " the greatest accumula- 
tion of local pressure is in the central area of the deep 
sea, while the greatest local relief takes place along the 
abraded coast lines. Here then should occur the chief 
volcanic vents." As the crust of the earth is much 
weaker on the coasts than elsewhere, it is more easily 
ruptured, and, as Mr. Babbage observes, immense rents 
might be produced there by its contraction in cooling 
down after being deprived of a portion of its original 
thickness. The pressure on the bottom of the ocean 
would force a column of lava mixed with ignited water 
and gas to rise through an opening thus formed, and, 
says Sir John Herschel, " when the column attains such 
a height that the ignited water can become steam, the 
joint specific gravity of the column is suddenly dimin- 
ished, and up comes a jet of mixed steam and lava, till 
so much has escaped that the matter deposited at the 
bottom of the ocean takes a fresh bearing, when the 
evacuation ceases and the crack becomes sealed up." 

This theory perfectly accords with the phenomena of 
nature, since there are very few active volcanos at a dis- 
tance from the sea, and the exceptions that do occur 
are generally near lakes, or they are connected with 
volcanos on the maritime coasts. Many break out even 
in the bottom of the ocean, probably owing to some of the 
supports of the superficial crust giving way, so that the 
eteam and lava are forced up through the fissures. 

Finally, Mr. Babbage observes that " in consequence 



SKCT. XXVI. SUPERFICIAL HEAT. 251 

of changes continually going on, by the destruction of 
forests, the filling up of seas, the wearing down of ele- 
vated lands, the heat radiated from the earth's surface 
varies considerably at different periods. In consequence 
of this variation, and also in consequence of the covering 
up of the bottom of the sea by the detritus of the land, 
the surfaces of equal temperature within the earth are 
continually changing their form, and exposing thick 
beds near the exterior to alterations of temperature. 
The expansion and contraction of these strata may form 
rents and veins, produce earthquakes, determine vol- 
canic eruptions, elevate continents, and possibly raise 
mountain chains." 

The numerous vents for the internal heat formed by 
volcanos, hot springs, and the emission of steam so 
frequent in volcanic regions, no doubt maintain the tran- 
quillity of the interior fluid mass, which seems to be 
perfectly inert unless when put in motion by unequal 
pressure. 

But to whatever cause tha increasing heat of the 
earth and the subterranean fires may ultimately be 
referred, it is certain that, except in some local in- 
stances, they have no sensible effect on the temperature 
of its surface. It may therefore be concluded that the 
heat of the earth above the zone of uniform temperature 
is entirely owing to the sun. 

The powe*of the solar rays depends much upon the 
manner in which they fall, as we readily perceive from 
the different climates on our globe. The earth is about 
three millions of miles nearer to the sun in winter than 
in summer, but the rays strike the northern hemi- 
sphere more obliquely hi winter than in the other half 
of the year. 

The observations of the north polar navigators, and 
those of Sir John Herscbel at the Cape of Good Hope, 
show that the direct heating influence of the solar rays 
is greatest at the equator, and that it diminishes gradu- 
ally as the latitude increases. At the equator the 
maximum is 48|, while in Europe it has never ex- 
ceeded 29i. 

M. Pouillet has estimated with singular ingenuity, 
from a series of observations made by himself, that the 



252 ISOGEOTHERMAL LINES. SECT. XXVI. 

whole quantity of heat which the earth receives annu- 
ally from the sun is such as would be sufficient to melt 
a stratum of ice covering the whole globe 46 feet deep. 
Part of this heat is radiated back into space ; but by far 
the greater part descends into the earth during the 
summer, toward the zone of uniform temperature, 
whence it returns to the surface in the course of the 
winter, and tempers the cold of the ground and the at- 
mosphere in its passage to the ethereal regions, where 
it is lost, or rather where it combines with the radiation 
from the other bodies of the universe in maintaining 
the temperature of space. The sun's power being 
greatest between the tropics, the caloric sinks deeper 
there than elsewhere, and the depth gradually dimin- 
ishes toward the poles ; but the heat is also transmitted 
laterally from the warmer to the colder strata north and 
south of the equator, and aids in tempering the severity 
of the polar regions. 

The mean heat of the earth above the stratum of 
constant temperature is determined from that of springs ; 
and if the spring be on elevated ground, the temperature 
is reduced by computation to what it would be at the 
level of the sea, assuming that the heat of the soil 
varies according to the' same law as the heat of the 
atmosphere, which is about 1 of Fahrenheit's ther- 
mometer for every 333-7 feet. From a comparison of 
the temperature of numerous springs witk that of the 
air, Sir David Brewster concludes that there is a par- 
ticular line passing nearly through Berlin, at which the 
temperature of springs and that of the atmosphere 
coincide ; that in approaching the arctic circle the tem- 
perature of springs is always higher than that of the air, 
while proceeding toward the equator it is lower. 

Since the warmth of the superficial strata of the earth 
decreases from the equator to the poles, there are many 
places in both hemispheres where the ground has the 
same mean temperature. If lines were drawn through 
all those points in the upper strata of the globe which 
have the same mean annual temperature, they would 
be nearly parallel to the equator between the tropics, 
and would become more and more irregular and sinuous 
toward the poles. These are called isogeothermal lines. 



SCT. XXVI. CLIMATE. 253 

A variety of local circumstances disturb their parallelism 
even between the tropics. 

The temperature of the ground at the equator is 
Jower on the coasts and islands than hi the interior of 
continents ; the warmest part is in the ulterior of Africa, 
but it is obviously affected by the nature of the soil, es- 
pecially if it be volcanic. 

Much has been done within a few years to ascertain 
the manner in which heat is distributed over the sur- 
face of our planet, and the variations of climate, which 
in a general view mean every change of the atmos- 
phere, such as of temperature, humidity, variations ot 
barometric pressure, purity of ah*, the serenity of the 
heavens, the effects of winds, and electric tension. 
Temperature depends upon the property which all 
bodies possess more or less, of perpetually absorbing and 
emitting or radiating heat. When the interchange is 
equal, the temperature of a body remains the same ; 
but when the radiation exceeds the absorption, it be- 
comes colder, and vice versa. In order to determine 
the distribution of heat over the surface of the earth, it 
is necessary to find a standard by which the tempera- 
ture in different latitudes may be compared. For that 
purpose it is requisite to ascertain by experiment the 
mean temperature of the day, of the month, and of the 
year, at as many places as possible throughout the 
earth. The annual average temperature may be found 
by adding the mean temperatures of all the months hi 
the year, and dividing the sum by twelve. The average 
of ten or fifteen years will give it with tolerable accu- 
racy ; for although the temperature in any place may 
be subject to very great variations, yet it never deviates 
more than a few degrees from its mean state, which 
consequently offers a good standard of comparison. 

If climate depended solely upon the heat of the sun, 
all places having the same latitude would have the same 
mean annual temperature. The motion of the sun in 
the ecliptic indeed occasions perpetual variations in the 
length of the day, and in the direction of the rays with 
regard to the earth; yet, as the cause is periodic, the 
mean annual temperature from the sun's motion alone 
must be constant in each parallel of latitude. For it is 
Y 



254 HEAT DECREASES WITH HEIGHT. SECT. XXVI. 

evident that the accumulation of heat in the long days of 
summer, which is but little diminished by radiation 
during the short nights, is balanced by the small quan- 
tity of heat received during the short days in winter, 
and its radiation in the long frosty and clear nights. 
In fact, if the globe were everywhere on a level with 
the surface of the sea, and of uniform substance, so as 
to absorb and radiate heat equally, the mean heat of the 
sun would be regularly distributed over its surface in 
zones of equal annual temperature parallel to the equa- 
tor, from which it would decrease to each pole as the 
square of the cosine of the latitude ; and its quantity 
would only depend upon the altitude of the sun and 
atmospheric currents. The distribution of heat, how- 
ever, in the same parallel, is very irregular in all lati- 
tudes except between the tropics, where the isothermal 
lines, or the lines passing through places of equal mean 
annual temperature, are more nearly parallel to the 
equator. The causes of disturbance are very numerous : 
but such as have the greatest influence, according to M. 
de Humboldt, to whom we are indebted for the greater 
part of what is known on the subject, are the elevation 
of the continents, the distribution of land and water 
over the surface of the globe exposing different absorb- 
ing and radiating powers ; the variations in the surface 
of the land, as forests, sandy deserts, verdant' plains, 
rocks, &c. ; mountain-chains covered with masses of 
snow, which diminish the temperature ; the reverbera- 
tion of the sun's rays in the valleys, which increases it; 
and the interchange of currents, both of air and water, 
which mitigates the rigor of climates ; the warm cur- 
rents from the equator softening the severity of the 
polar frosts, and the cold currents from the poles tem- 
pering the intense heat of the equatorial regions. To 
these may be added cultivation, though its influence 
extends over but a small portion of the globe, only a 
fourth part of the land being inhabited. 

Temperature decreases with the height above the 
level of the sea, as well as with the latitude. The air 
in the higher regions of the atmosphere is much cooler 
than that below, because the warm air expands as it 
rises, by which its capacity for heat is increased, a great 



SCT. XXVI. LINE OF PERPETUAL SNOW. 255 

proportion becomes latent, and less of it sensible. A 
portion of air at the surface of the earth whose temper- 
ature is 70 of Fahrenheit, if carried to the height of 
two miles and a half, would expand so much that its tem- 
perature would be reduced 50 ; and in the ethereal 
regions the temperature is 90 below the point of con- 
gelation. 

The height at which snow lies perpetually decreases 
from the equator to the poles, and is higher in summer 
than in winter ; but it varies from many circumstances. 
Snow rarely falls when the cold is intense and the at- 
mosphere dry. Extensive forests produce moisture by 
their evaporation ; and high table-lands, on the contrary, 
dry and warm the ah*. In the Cordilleras of the Andes, 
plains of only twenty-five square leagues raise the tem- 
perature as much as 3 or 4 above what is found at the 
same altitude on the rapid declivity of a mountain, con- 
sequently the line of perpetual snow varies according as 
one or other of these causes prevails. Aspect in gen- 
eral has also a great influence ; yet, according to M. 
Jacquemont, the line of perpetual snow is much higher 
on the northern than on the southern side of the Hima- 
laya mountains. On the whole, it appears that the mean 
height between the tropics at which the snow lies per- 
petually is about 15,207 feet above the level of the sea ; 
whereas snow does not cover the ground continually at 
the level of the ocean till near the north pole. In the 
southern hemisphere, however, the cold is greater than 
in the northern. In Sandwich Land, between the 54th 
and 58th degrees of latitude, perpetual snow and ice ex- 
tend to the sea-beach ; and in the island of St. George's, 
in the 53rd degree of south latitude, which corresponds 
with the latitude of the central counties of England, per- 
petual snow descends even to the level of the ocean. It 
has been shown that this excess of cold in the southern 
hemisphere cannot be attributed to the winter being 
longer than ours by 7| days. It is probably owing to 
the ice being more extensive at the south than the north 
pole, and to the open sea surrounding it, which permits 
the icebergs to descend to a lower latitude by 10 than 
they do in the northern hemisphere, on account of the 
numerous obstructions opposed to them by the islands 



256 EFFECTS OF THE OCEAN. SKCT. XXVI. 

and continents about the north pole. Icebergs seldom 
float farther to the south than the Azores ; whereas 
those that come from the south pole descend as far as 
the Cape of Good Hope, and occasion a continual ab- 
sorption of heat in melting. 

The influence of mountain-chains does not wholly 
depend upon the line of perpetual congelation. They 
attract and condense the vapors floating in the air, and 
send them down in torrents of rain. They radiate heat 
into the atmosphere at a lower elevation, and increase 
the temperature of the valleys by the reflection of the 
sun's rays, and by the shelter they afford against pre- 
vailing winds. But on the contrary, one of the most 
general and powerful causes of cold arising from the vi- 
cinity of mountains, is the freezing currents of wind 
which rush from their lofty peaks along the rapid decliv- 
ities, chilling the surrounding valleys : such is the cut- 
ting north wind called the bise in Switzerland. 

Next to elevation, the difference in the radiating and 
absorbing powers of the sea and land has the greatest 
influence in disturbing the regular distribution of heat. 
The extent of the dry land is not above the fourth part 
of that of the ocean ; so that the general temperature 
of the atmosphere, regarded as the result of the partial 
temperatures of the whole surface of the globe, is most 
powerfully modified by the sea. Besides, the ocean 
acts more uniformly on the atmosphere than the diver- 
sified surface of the solid mass does, both by the equality 
of its curvature and its homogeneity. In opaque sub- 
stances the accumulation of heat is confined to the 
stratum nearest the surface. The seas become less 
heated At their surface than the land, because the solar 
rays, before being extinguished, penetrate the trans- 
parent liquid to a greater depth and in greater numbers 
than in the opaque masses. On the other hand, water 
has a considerable radiating power, which, together 
with evaporation, would reduce the surface of the ocean 
to a very low temperature, if the cold particles did not 
sink to the bottom on account of their superior density. 
The seas preserve a considerable portion of the heat 
they receive in summer, and from their saltness do not 
freeze so soon as fresh water. So that in consequence 



SKCT. XXVI. TEMPERATURE OF THE LAND. 257 

of all these circumstances, the ocean is not subject to 
such variations of heat as the land ; and by imparting 
its temperature to the winds, it diminishes the rigor of 
climate on the coasts and in the islands, which are 
never subject to such extremes of heat and cold as are 
experienced in the interior of continents, though they 
are liable to fogs and rain from the evaporation of the 
adjacent seas. On each side of the equator to the 48th 
degree of latitude, the surface of the ocean is in gene- 
ral warmer than the air above it. The mean of the 
difference of the temperature at noon and midnight is 
about l-37, the greatest deviation never exceeding from 
0-36 to 2'16, which is much cooler than the air over 
the land. 

On land the. temperature depends upon the nature 
of the soil and its products, its habitual moisture or dry- 
ness. From the eastern extremity of the Sahara 
desert quite across Africa, the soil is almost entirely 
barren sand ; and the Sahara desert itself, without in- 
cluding Dafour or Dongola, extends over an area of 
194,000 square leagues, equal to twice the area of the 
Mediterranean Sea, and raises the temperature of the 
air by radiation from 90 to 100, which must have a 
most extensive influence. On the contrary, vegetation 
cools the air by evaporation and the apparent radiation 
of cold from the leaves of plants, because they absorb 
more caloric than they give out. The graminiferous 
plains of South America cover an extent ten times 
greater than France, occupying no less than about 
50,000 square leagues, which is more than the whole 
chain of the Andes, and all the scattered mountain- 
groups of Brazil. The'se, together with the plains of 
North America and the steppes of Europe and Asia, 
must have an extensive cooling effect on the atmosphere 
if it be considered that in calm and serene nights they 
cause the thermometer to descend 12 or 14, and that 
in the meadows and heaths in England the absorption 
of heat by the grass is sufficient to cause the tempera- 
ture to sink to the point of congelation during the night 
for ten months in the year. Forests cool the air also 
by shading the ground from the rays of the sun, and by 
evaporation from the boughs. Hales found that the 
17 Y 2 



258 CONFIGURATION OF LAND AND WATER. SECT. XXVI. 

leaves of a single plant of helianthus three feet high ex- 
posed nearly forty feet of surface ; and if it be con- 
sidered that the woody regions of the river Amazons, 
and the higher part of the Oroonoko, occupy an area of 
260,000 square leagues, some idea may be formed of 
the torrents of vapor which rise from the leaves of the 
forests all over the globe. However, the frigorific 
effects of their evaporation are counteracted in some 
measure by the perfect calm which reigns in the tropi- 
cal wildernesses. The innumerable rivers, lakes, pools, 
and marshes interspersed through the continents absorb 
caloric, and cool the air by evaporation ; but on account 
of the chilled and dense particles sinking to the bottom, 
deep water diminishes the cold of winter, so long as ice 
is not formed. 

In consequence of the difference in the radiatmg and 
absorbing powers of the sea and land, their configuration 
greatly modifies the distribution of heat over the surface 
of the globe. Under the equator only one- sixth part of 
the circumference is land ; and the superficial extent of 
land in the northern and southern hemispheres is in the 
proportion of three to one. The effect of this unequal 
division is greater in the temperate than in the torrid 
zones, for the area of land iu the northern temperate 
zone is to that in the southern as thirteen to one, where- 
as the proportion of land between the equator and each 
tropic is as five to four. It is a curious fact noticed by 
Mr. Gardner, that only one twenty-seventh part of the 
land of the globe has land diametrically opposite to it. 
This disproportionate arrangement of the solid part of 
the globe has a powerful influence on the temperature 
of the southern hemisphere. But besides these greater 
modifications, the peninsulas, promontories, and capes, 
running out into the ocean, together with bays and in- 
ternal seas, all affect temperature. To these may be 
added the position of continental masses with regard to 
the cardinal points. All these diversities of land and 
water influence temperature by the agency of the winds. 
On this account the temperature is lower on the eastern 
coasts both of the New and Old World than on the 
western ; for considering Europe as an island, the gen- 
eral temperature is mild in proportion as the aspect is 



SECT. XXVI. ISOTHERMAL LINES. 259 

open to the western ocean, the superficial temperature 
of which, as far north as the 45th and 50th degrees of 
latitude, does not fall below 48 or 51 of Fahrenheit, 
even in the middle of winter. On the contrary, the 
cold of Russia arises from its exposure to the northern 
and eastern winds. But the European part of that em- 
pire has a less rigorous climate than the Asiatic, because 
it does not extend to so high a latitude. 

The interposition of the atmosphere modifies all the 
effects of the sun's heat. The earth communicates its 
temperature so slowly that M. Arago has occasionally 
found as much as from 14 to 18 of difference between 
the heat of the soil and that of the air two or three 
inches above it. 

The circumstances which have been enumerated, and 
many more, concur in disturbing the regular distribution 
of heat over the globe, and occasion numberless local ir- 
regularities. Nevertheless the mean annual temperature 
becomes gradually lower from the equator to the poles. 
But the diminution of mean heat is most rapid between 
the 40th and 45th degrees of latitude both in Europe 
and America, which accords perfectly with theory; 
whence it appears that the variation in the square of 
the cosine of the latitude (N. 123), which expresses the 
law of the change of temperature, is a maximum to- 
ward the 45th degree of latitude. The mean annual 
temperature under the line in America is about 81^ of 
Fahrenheit : in Africa it is said to be nearly 83. "The 
difference probably arises from the winds of Siberia and 
Canada, whose chilly influence is sensibly felt in Asia 
and America, even within 18 of the equator. 

The isothermal lines are nearly parallel to the equator, 
till about the 22d degree of latitude on each side of it, 
where they begin to lose their parallelism, and continue 
to do so more and more as the latitude augments. 
With regard to the northern hemisphere, the isother- 
mal line of 59 of Fahrenheit passes between Rome and 
Florence in latitude 43 ; and near Raleigh in North 
Carolina, latitude 36 : that of 50 of equal annual tem- 
perature runs through the Netherlands, latitude 51; 
and near Boston in the United States, latitude 42 : 
that of 41 passes near Stockholm, latitude 59| ; and 



260 ISOTHERMAL LINES. SECT. XXVI. 

St. George's Bay, Newfoundland, latitude 48 : and 
lastly, the line of 32, the freezing point of water, passes 
between Ulea in Lapland, latitude 66, and Table Bay, 
on the coast of Labrador, latitude 54. 

Thus it appears that the isothermal lines, which are 
nearly parallel to the equator for about 22, afterward 
deviate more and more. From the observations of Sir 
Charles Giesecke in Greenland, of Captain Scoresby in 
the Arctic Seas, and also from those of Sir Edward 
Parry and Sir John Franklin, it is found that the iso- 
thermal lines of Europe and America entirely separate 
in the high latitudes, and surround two poles of max- 
imum cold, one in America and the other in the north 
of Asia, neither of which coincides with the pole of the 
earth's rotation. These poles are both situate in about 
the 80th parallel of north latitude. The transatlantic 
pole is in the 100th degree of west longitude, about 
5 to the north of Sir Graham Moore's Bay, in the 
Polar Seas ; and the Asiatic pole is in the 95th degree 
of east longitude, a little to the north of the Bay of Tai- 
mura, near the North-east Cape. According to the 
estimation of Sir David Brewster, from the observations 
of M. de Humboldt and Captains Parry and Scoresby, 
the mean annual temperature of the Asiatic pole is 
nearly 1 of Fahrenheit's thermometer, and that of the 
transatlantic pole about 3^ below zero, whereas he sup- 
poses the mean annual temperature of the pole of rota- 
tion to be 4 or 5. It is believed that two correspond- 
ing poles of maximum cold exist in the southern hemis- 
phere, though observations are wanting to trace the 
course of the southern isothermal lines with the same 
accuracy as the northern. 

The isothermal lines, or such as pass through places 
where the mean annual temperature of the air is the 
same, do not always coincide with the isogeothermal 
lines, which are those passing through places where the 
mean temperature of the ground is the same. Sir 
David Brewster, in discussing this subject, finds that 
the isogeothermal lines are always parallel to the iso- 
thermal lines ; consequently the same general formula 
will serve to determine both, since the difference is a 
constant quantity obtained by observation, and depend- 



SECT. XXVI. EXCESSIVE CLIMATES. 261 

ing upon the distance of the place from the neutral iso- 
thermal line. These results are confirmed by the ob- 
servations of M. Kupffer of Kasan during his excursions 
to the north, which show that the European and the 
American portions of the isogeothermal line of 32 of 
Fahrenheit actually separate, and go round the two 
poles of maximum cold. This traveler remarked, also, 
that the temperature both of the air and of the soil de- 
creases most rapidly toward the 45th degree of latitude. 

It is evident that places may have the same mean an- 
nual temperature, and yet differ materially in climate. 
In one, the winters may be mild, and the summers cool ; 
whereas another may experience the extremes of heat 
and cold. Lines passing through places having the 
same mean summer or winter temperature, are neither 
parallel to the isothermal, the geothermal lines, nor to one 
another, and they differ still more from the parallels of 
latitude. In Europe, the latitude of two places which 
have the same annual heat never differs more than 8 or 
9 ; whereas the difference in the latitude of those having 
the same mean winter temperature is sometimes as 
much as 18 or 19. At Kasan in the interior of Rus- 
sia, in latitude 55-48, nearly the same with that of 
Edinburgh, the mean annual temperature is about 37-6 ; 
at Edinburgh it is 47-84. At Kasan, the mean sum- 
mer temperature is 64-84, and that of winter 2-12; 
whereas at Edinburgh the mean summer temperature 
is 58-28, and that of winter 38-66. Whence it ap- 
pears that the difference of winter temperature is much 
greater than that of summer. At Quebec, the sum- 
mers are as warm as those in Paris, and grapes some- 
times ripen in the open air : whereas the winters are 
as severe as in Petersburgh ; the snow lies five feet 
deep for several months, wheel carriages cannot be used, 
the ice is too hard for skating, traveling is performed in 
sledges, and frequently on the ice of the river St. Law- 
rence. The cold at Melville Island on the 15th of Jan- 
uary, 1820, according to Sir Edward Parry, was 55 
below the zero of Fahrenheit's thermometer, only 3 
above the temperature of the ethereal regions, yet the 
summer heat in these high latitudes is insupportable. 

Observations tend to prove that all the climates of the 



2G.2 INFLUENCE OF HEAT ON VEGETATION. SKCT. XXVII. 

earth are stable, and that their vicissitudes are only 
periods or oscillations of more or less extent, which van- 
ish in the mean annual temperature of a sufficient num- 
ber of years. This constancy of the mean annual temper- 
ature of the different places on the surface of the globe 
shows that the same quantity of heat, which is annually 
received by the earth, is annually radiated into space. 
Nevertheless a variety of causes may disturb the climate 
of a place; cultivation may make it warmer; but it is 
at the expense of some other place, which becomes 
colder in the same proportion. There may be a suc- 
cession of cold summers and mild winters, but in some 
other country the contrary takes place to effect the 
compensation ; wind, rain, snow, fog, and the other me- 
teoric phenomena, are the ministers employed to accom- 
plish the changes. The distribution of heat may vary 
with a variety of circumstances ; but the absolute quan- 
tity lost and gained by the whole earth in the course of 
a year is invariably the same. 



SECTION XXVII. 

Influence of Temperature on Vegetation Vegetation varies with the Lati 
tude and Height above the Sea Geographical Distribution of Land 
Plants Distribution of Marine Plants Corallines, Shell-fish, Reptiles, 
Insects, Birds, and Quadrupeds Varieties of Mankind, yet Identity of 
Species. 

THE gradual decrease of temperature in the air and in 
the earth, from the equator to the poles, is clearly indi- 
cated by its influence on vegetation. In the valleys of 
the torrid zone, where the mean annual temperature is 
very high, and where there is abundance of light and 
moisture, nature adorns the soil with all the luxuriance 
of perpetual summer. The palm, the bombax ceiba, 
and a variety of magnificent trees, tower to the height 
of 150 or 200 feet above the banana, the bamboo, the 
arborescent fern, and numberless other tropical produc- 
tions, so interlaced by creeping and parasitical plants as 
often to present an impenetrable barrier. But the 
richness of vegetation gradually diminishes with the tem- 
perature the splendor of the tropical forest is succeeded 



SECT. XXVII. LIGHT REQUISITE FOR PLANTS. 263 

by the regions of the olive and vine ; these again yield 
to the verdant meadows of more temperate climes ; then 
follow the birch and the pine, which probably owe their 
existence in very high latitudes more to the warmth of 
the soil than to that of the air. But even these enduring 
plants become dwarfish stunted shrubs, till a verdant 
carpet of mosses and lichens, enameled with flowers, 
exhibits the last sign of vegetable life during the short 
but fervent summers at the polar regions. Such is the 
effect of cold and diminished light on the vegetable king- 
dom, that the number of species growing under the 
line, and in the northern latitudes of 45 and 68, are in 
the proportion of the numbers 12, 4, and 1. Notwith- 
standing the remarkable difference between a tropical 
and polar Flora, light and moisture seem to be almost the 
only requisites for vegetation, since neither heat, cold, 
nor even comparative darkness, absolutely destroy the 
fertility of nature. In salt plains and sandy deserts 
alone, hopeless barrenness prevails. JPlants grow on the 
borders of hot springs they form the oasis wherever 
moisture exists, among the burning sands of Africa 
they are found in caverns almost void of light, though 
generally blanched and feeble. The ocean teems with 
vegetation. The snow itself not only produces a red 
alga, discovered by Saussure in the frozen declivities of 
the Alps, found in abundance by the author crossing 
the Col de Bonhomme from Savoy to Piedmont, and by 
the polar navigators in the Arctic regions, but it affords 
shelter to the productions of those inhospitable climes 
against the piercing winds that sweep over fields of ever- 
lasting ice. Those interesting mariners narrate, that 
ander this cold defence plants spring up, dissolve the 
snow a few inches round, and the part above being 
again quickly frozen into a transparent sheet of ice, ad- 
mits the sun's rays, which warm and cherish the plants 
in this natural hot-house, till the returning summer ren- 
ders such protection unnecessary. 

The chemical action of light is, however, absolutely 
requisite for the growth of plants which derive their 
principal nourishment from the atmosphere. They con- 
sume carbonic acid gas, vapor, nitrogen, and the ammo- 
nia it contains ; but it is the chemical agency of light 



264 DISTRIBUTION OF PLANTS. SECT. XXVII. 

that enables them to absorb, decompose, and consolidate 
these substances into wood, leaves, flowers, and fruit. 
The atmosphere would soon be deprived of these ele- 
ments of vegetable life, were they not perpetually sup- 
plied by the animal creation ; while in return, plants 
decompose the moisture they imbibe, and having assim- 
ilated the carbonic acid gas, they exhale oxygen for the 
maintenance of the animated creation, and thus preserve 
a just equilibrium. Hence it is the powerful and com- 
bined influences of the whole solar beams that give such 
brilliancy to the tropical forests, while with their de- 
creasing energy in the higher latitudes, vegetation be- 
comes less and less vigorous. 

By far the greater part of the hundred and ten thou- 
sand known species of plants are indigenous in Equinoctial 
America. Europe contains about half the number ; Asia 
with its islands, somewhat less than Europe; New 
Holland with the islands in the Pacific, still less ; and in 
Africa there are fewer vegetable productions than in 
any part of the globe of equal extent. Very few social 
plants, such as grasses and heaths, that cover large 
tracts of land, are to be found between the tropics, ex- 
cept on the sea-coasts and elevated plains : some excep- 
tions to this, however, are to be met with in the jungles 
of the Deccan, Khandish, &c. In the equatorial regions, 
where the heat is always great, the distribution of plants 
depends upon the mean annual temperature ; whereas 
in temperate zones the distribution is regulated in some 
dogree by the summer heat. Some plants require a 
gentle warmth of long continuance, others flourish most 
where the extremes of heat and cold are greater. The 
range of wheat is very great : it may be cultivated as far 
north as the 60th degree of latitude, but in the ton-id 
zone it will seldom form an ear below an elevation of 
4500 feet above the level of the sea, from exuberance of 
vegetation ; nor will it ripen above the height of 10,800 
feet, though much depends upon local circumstances. 
Colonel Sykes states that in the Deccan wheat thrives 
1800 feet above the level of the sea. The best wines 
are produced between the 30th and 45th degrees of 
north latitude. With regard to the vegetable kingdom, 
elevation is equivalent to latitude, as far as temperature 



SICT. XXVII. DISTRIBUTION OF PLANTS. 265 

is concerned. In ascending the mountains of the torrid 
zone, the richness of the tropical vegetation diminishes 
with the height ; a succession of plants similar to, though 
not identical with, those found in latitudes of corre- 
sponding mean temperature takes place ; the lofty for- 
ests by degrees lose their splendor, stunted shrubs suc- 
ceed, till at last the progress of the lichen is checked by 
eternal snow. On the volcano of TenerifFe there are 
five successive zones, each producing a distinct race of 
plants. The first is the region of vines, the next that 
of laurels ; these are followed by the districts of pines, 
of mountain broom, and of grass ; the whole covering the 
declivity of the peak through an extent of 11,200 feet of 
perpendicular height. 

Near the equator, the oak flourishes at the height of 
9200 feet above the level of the sea, and on the lofty 
range of the Himalaya, the primula, the convallaria, and 
the veronica blossom, but not the primrose, the lily of 
the valley, or the veronica which adorn our meadows : 
for although the herbarium collected by Mr. Moorcroft, 
on his route from Neetee to Daba and Garlope in Chi- 
nese Tartary, at elevations as high or even higher than 
Mont Blanc, abounds in Alpine and European genera, 
the species are universally different, with the single 
exception of the rhodiola rosea, which is identical with 
the species that blooms in Scotland. It is not in this 
instance alone that similarity of climate obtains without 
identity of productions ; throughout the whole globe, a 
certain analogy both of structure and appearance is fre- 
quently discovered between plants under corresponding 
circumstances, which are yet specifically different. It 
is even said that a distance of 25 of latitude occasions a 
total change, not only of vegetable productions, but of 
organized beings. Certain it is, that each separate re- 
gion both of land and water, from the frozen shores of 
the polar circles to the burning regions of the torrid 
zone, possesses a Flora of species peculiarly its own. 
The whole globe has been divided by botanical geogra- 
phers into twenty-seven botanical districts differing al- 
most entirely in their specific vegetable productions ; the 
limits of which are most decided when they are sepa- 
rated by a wide expanse of ocean, mountain-chains, 
Z 



266 DISTRIBUTION OF PLANTS. SECT. XXVII. 

sandy deserts, salt plains, or internal seas. A consider- 
able number of plants are common to the northern re- 
gions of Asia, Europe, and America, where the continents 
almost unite ; but in approaching the south, the Floras 
of these three great divisions of the globe differ more 
and more even in the same parallels of latitude, which 
shows that temperature alone is not the cause of the al- 
most complete diversity of species that everywhere pre- 
vails. The Floras of China, Siberia, Tartary, of the 
European district including Central Europe, and the 
coast of the Mediterranean, and the Oriental region, 
comprising the countries round the Black and Caspian 
Seas, all differ in specific character. Only twenty -four 
species were found by MM. Bonpland and Humboldtin 
Equinoctial America identical with those of the old 
world: and Mr. Brown not only found that a peculiar 
vegetation exists in New Holland, between the 33d and 
35th parallels of south latitude, but that, at the eastern 
and western extremities of these parallels, not one spe- 
cies is common to both, and that certain genera also are 
almost entirely confined to these spots. The number of 
species common to Australia and Europe are only 166 
out of,4100, and probably some of these have been con- 
veyed thither by the colonists. This proportion exceeds 
what is observed in Southern Africa, and from what has 
been already stated, the proportion of European species 
in Equinoctial America is still less. 

Islands partake of the vegetation of the nearest con- 
tinents, but when very remote from land their Floras 
are altogether peculiar. The Aleutian Islands, extend- 
ing between Asia and America, partake of the vegeta- 
tion of the northern parts of both these continents, and 
may have served as a channel of communication. In 
Madeira and Teneriffe, the plants of Portugal, Spain, 
the Azores, and of the north coast of Africa are found ; 
and the Canaries contain a great number of plants be- 
longing to the African coast. But each of these islands 
possesses a Flora that exists nowhere else ; and St. 
Helena, standing alone in the midst of the Atlantic 
Ocean, out of sixty-one indigenous species, produces 
only two or three recognized as belonging to any other 
part of the world. 



SECT. XXVII. DISTRIBUTION OF MARINE PLANTS. 267 

Tt appears from the investigations of M. de Humboldt, 
that between the tropics the monocotyledonous plants, 
such as grasses and palms which have only one seed- 
lobe, are to the dicotyledonous tribe, which have two 
seed-lobes like most of the European species, in the 
proportion of one to four ; in the temperate zones they 
are as one to six; and in the Arctic regions, where 
mosses and lichens which form the lowest order of the 
vegetable creation abound, the proportion is as one to 
two. The annual monocotyledooous and dicotyledonous 
plants in the temperate zones amount to one-sixth of 
the whole, omitting the Cryptogamia (N. 214) ; in the 
torrid zone they scarcely form one-twentieth, and in 
Lapland one-thirtieth part. In approaching the equa- 
tor, the ligneous exceed the number of herbaceous 
plants, in America there are a hundred and twenty 
different species of forest trees, whereas in the same 
latitudes in Europe only thirty-four are to be found. 

Similar laws appear to regulate the distribution of 
marine plants. M. Lamouroux has discovered that the 
groups of algae, or marine plants, affect particular tem- 
peratures or zones of latitude, though some few genera 
prevail throughout the ocean. The polar Atlantic basin, 
to the 40th degree of north latitude, presents a well-de- 
fined vegetation. The West Indian seas, including the 
Gulf of Mexico, the eastern coast of South America, the 
Indian Ocean and its gulfs, the shores of New Holland, 
and the neighboring islands, have each their distinct 
species. The Mediterranean possesses a vegetation 
peculiar to itself, extending to the Black Sea ; and the 
species of marine plants on the coast of Sj^ia and in 
the port of Alexandria differ almost entirely from those 
of Suez and the Red Sea, notwithstanding the proxim- 
ity of their geographical situation. It is observed that 
shallow seas have a different set of plants from such as 
are deeper and colder; and, like terrestrial vegetation, 
the algae are most numerous toward the equator, where 
the quantity must be prodigious, if we may judge from 
the gulf-weed, which certainly has its origin in the 
tropical seas, and is drifted, though not by the gulf- 
stream, to higher latitudes, where it accumulates in such 
quantities, that the early Portuguese navigators, Colum- 



268 DISTRIBUTION OF MARINE PLANTS. SECT. XXVII. 

bus and Lerius, compared the sea to extensively inun- 
dated meadows, in which it actually impeded their ships 
and alarmed their sailors. M. de Humboldt, in his 
Personal Narrative, mentions that the most extensive 
bank of sea-weed is in the northern Atlantic, a little 
west of the meridian of Fayal, one of the Azores, be- 
tween the 25th and 36th degrees of latitude. Vessels 
returning to Europe from Monte Video, or from the 
Cape of Good Hope, cross this bank nearly at an equal 
distance from the Antilles and Canary Islands. The 
other bank occupies a smaller space, between the 22d 
and 26th degrees of north latitude, about eighty leagues 
west of the meridian of the Bahama Islands, and is gen- 
erally traversed by vessels on their passage from the 
Caicos to the Bermuda Islands. These masses consist 
chiefly of one or two species of Sargassum, the most ex- 
tensive genus of the order Fucoideae. 

Some of the sea- weeds grow to the enormous length 
of several hundred feet, and all are highly colored, 
though many of them must grow in the deep caverns of 
the ocean, in total or almost total darkness ; light how- 
ever may not be the only principle on which the color of 
vegetables depends, since M. de Humboldt met with 
green plants growing in complete darkness at the bottom 
of one of the mines at Freyberg. 

It appears that in the dark and tranquil caves of the 
ocean, on the shores alternately covered and deserted by 
the restless waves, on the lofty mountain and extended 
plain, in the chilly regions of the north and in the genial 
warmth of the south, specific diversity is a general law 
of the vegqjplble kingdom, which cannot be accounted for 
by diversity of climate : and yet the similarity, though 
not identity, of species is such, under the same isother- 
mal lines, that if the number of species belonging to one 
of the great families of plants be known in any part of 
the globe, the whole number of the phanerogamous or 
more perfect plants, and also the number of species com- 
posing the other vegetable families, may be estimated 
with considerable accuracy. 

Various opinions have been formed on the original or 
primitive distribution of plants over the surface of the 
globe ; but since botanical geography became a regular 



SKCT. XXVH. DISTRIBUTION OF ANIMALS. 269 

science, the phenomena observed have led to the con- 
clusion that vegetable creation must have taken place in 
a number of distinctly different centers, each of which 
was the original seat of a certain number of peculiar 
species, which at first grew there and nowhere else. 
Heaths are exclusively confined to the Old World, and 
no indigenous rose-tree has ever been discovered in the 
New; the whole southern hemisphere being destitute 
of that beautiful and fragrant plant. But this is still 
more confirmed by multitudes of particular plants hav- 
ing an entirely local and insulated existence, growing 
spontaneously in some particular spot and in no other 
place ; for example, the cedar of Lebanon, which grows 
indigenously on that mountain, and in no other part of 
the world. On the other hand, as there can be no doubt 
but that many races of plants have been extinguished, 
Sir John Herschel thinks it possible that these solitary 
instances may be the last surviving remnants of the 
same groups universally disseminated, but in course of 
extinction ; or that perhaps two processes may be going 
on at the same time ; " some groups may be spreading 
from their foci, others retreating to their last strong- 
holds." 

The same laws obtain in the distribution of the ani- 
mal creation. The zoophyte (N. 215), occupying the 
lowest place in animated nature, is widely scattered 
through the seas of the torrid zone, each species being 
confined to the district best fitted to its existence. 
Shell-fish decrease in size and beauty with their dis- 
tance from the equator ; and as far as is known, each 
sea has its own kind, and every basin of thelpean is in- 
habited by its peculiar tribe of fish. Indeed MM. Peron 
and Le Sueur assert, that among the many thousands 
of marine animals which they had examined, there is 
not a single animal of the southern regions which is not 
distinguishable by essential characters from the analo- 
gous species in the northern seas. Reptiles are not 
exempt from the general law. The saurian (N. 216) 
tribes of the four quarters of the globe differ in species ; 
and although warm countries abound in venomous 
snakes, they are specifically different, and decrease both 
in numbers and in the virulence of their poison with de- 



270 MANKIND IDENTICAL IN SPECIES. SECT. XXVII. 

crease of temperature. The dispersion of insects ne- 
cessarily follows that of the vegetables which supply 
them with food ; and in general it is observed, that each 
kind of plant is peopled by its peculiar inhabitants. 
Each species of bird has its particular haunt, notwith- 
standing the locomotive powers of the winged tribes. 
The emu is confined to Australia, the condor never 
leaves the Andes, nor the great eagle the Alps ; and 
although some birds are common to every country, they 
are few in number. Quadrupeds are distributed in the 
same manner wherever man has not interfered. Such 
as are indigenous in one continent are not the same with 
their congeners in another ; and with the exception of 
some kinds of bats, no warm-blooded animal is indigenous 
v in the Polynesian Archipelago, nor in any of the islands 
on the borders of the central part of the Pacific. 

In reviewing the infinite variety of organized beings 
that people the surface of the globe, nothing is more re- 
markable than the distinctions which characterize the 
different tribes of mankind, from the ebony skin of the 
torrid zone to the fair and ruddy complexion of Scandi- 
navia a difference which existed in the earliest recorded 
times, since the African is represented in the Sacred 
Writings to have been as black as he is at the present 
day, and the most ancient Egyptian paintings confirm 
that truth ; yet it appears from a comparison of the 
principal circumstances relating to the animal economy 
or physical character of the various tribes of mankind, 
that the different races are identical in species. Many 
attempts have been made to trace the various tribes 
back to ^pommon origin, by collating the numerous 
languages^vhich are or have been spoken. Some 
classes of these have few or no words in common, yet 
exhibit a remarkable analogy in the laws of their gram- 
matical construction. The languages spoken by the 
native American nations afford examples of these ; in- 
deed the refinement in the grammatical construction of 
the tongues of the American savages leads to the belief, 
that they must originally have been spoken by a much 
more civilized class of mankind. Some tongues have 
little or no resemblance in structure, though they cor- 
respond extensively in their vocabularies, as the Syrian 



SKCT. XXV1U. INFLUENCE OF ELECTRICITY. 271 

dialects. In all of these cases it may be inferred, that 
the nations speaking the languages in question are de- 
scended from the same stock ; but the probability of a 
common origin is much greater in the Indo-European 
nations, whose, languages, such as the Sanscrit, Greek, 
Latin, German, &c., have an affinity both in structure 
and correspondence of vocables. In many tongues* not 
the smallest resemblance can be traced ; length of time, 
however, may have obliterated origiAd -identity. The 
conclusion drawn from the whole investigation is, that 
although the distribution of organized beings does not 
follow the direction of the isothermal lines, temperature 
has a very great influence on their physical development. 
The heat of the air is so intimately connected with its 
electrical condition, that electricity must also affect the 
distribution of plants and animals over the face of the 
earth, the more so as it seems to have a great share in 
the functions of animal and vegetable life. It is the sole 
cause of many atmospheric and terrestrial phenomena, 
and performs an important part in the economy of nature. 



SECTION XXVIII. 

Of ordinary Electricity, generally called Electricity of Tension Methods 
of exciting Bodies Transference Electrics and Non-ElectricsLaw of 
its Intensity Distribution Tension Electric Heat and Light Atmos- 
pheric Electricity Its Cause Electric Clouds Back Stroke Violent 
Effects of Lightning Its Velocity Phosphorescence Phosphorescent 
Action of Solar Spectrum Aurora. 

ELECTRICITY is one of those imponderable agents 
pervading the earth and all substances, witl^lt affecting 
their volume or temperature, or even givin^my visible 
sign of its existence when in a latent state ; but when 
elicited developing forces capable of producing the most 
sudden, violent, and destructive effects in some cases, 
while in others their action, though less energetic, is of 
indefinite and uninterrupted continuance. These modi- 
fications of the electric force, incidentally depending 
upon the manner in which it is excited, present phe- 
nomena of great diversity, but yet so connected as to 
justify the conclusion that they originate in a common 
principle. 



272 ELECTRICS. 

Electricity may be called into activity by mechanical 
power, by chemical action, by heat, and by magnetic 
influence. We are totally ignorant why it is roused 
from its neutral state by such means, or of the manner 
of its existence in bodies, whether it be a-material agent, 
vibrations of ether, or merely a property of matter. 
Various circumstances render it more than probable 
that, like light and heat, it is a modification or vibration 
of that subtile etlftreaT medium which in a highly elas- 
tic state pervades all space, and which is capable of 
moving with various degrees of facility through the pores 
even of the densest substances. As experience shows 
that bodies in one electric state attract, and in another 
repel each other, the hypothesis of two fluids has been 
adopted by many philosophers ; but probably the mutual 
attraction and repulsion of bodies arise from the redun- 
dancy and defect of their electricities, though all the 
electrical phenomena can be explained on either hy- 
pothesis. Bodies having a redundancy of the electric 
fluid are said to be positively electric, and those in defect 
negatively. As each kind of electricity has its peculiar 
properties, the science may be divided into four branch- 
es, of which the following notice is intended to convey 
some idea. 

Substances in a neutral state neither attract nor 
repel. There is a numerous class called electrics, 
in which the electric equilibrium is destroyed by fric- 
tion ; then the positive and negative electricities are 
called into action or separated ; the positive is im- 
pelled in one direction, and the negative in another ; 
or more jflfcrectly, the electricity is impelled in one di- 
rection, at^ie expense of the other where there is a de- 
ficiency of it. .Electricities of the same kind repel, 
whereas those of different kinds attract each other. 
The attractive power is exactly equal to the repulsive 
power at equal distances, and when not opposed, they 
coalesce .with great rapidity and violence; producing 
the electric flash, explosion, and shock : then equili- 
brium is restored, and the electricity remains latent till 
again called forth by a new exciting cause. One kind 
of electricity cannot be evolved without the evolution of 
an equal quantity of the opposite kind. Thus when u 



SECT. XXVIII. NON-ELECTRICS. 273 

glass rod is rubbed with a piece of silk, as much positive 
electricity is elicited in the glass as there is negative in 
the silk ; or in other words there is a redundancy in the 
glass and a proportional deficiency in the silk. The 
kind of electricity depends more upon the mechanical 
condition than on the nature of the surface : for when 
two plates of glass, one polished and the other rough, 
are rubbed against each other, the polished surface ac- 
quires positive and the rough negative electricity ; that 
is, the one gains and the other loses. The manner in 
which friction is performed also alters the kind of elec- 
tricity. Equal lengths of black and white riband ap- 
plied longitudinally to one another, and drawn between 
the finger and thumb, so as to rub their surfaces to- 
gether, become electric. When separated, the white 
riband is found to have acquired positive electricity, and 
the black has lost it, or become negative : but if the 
whole length of the black riband be drawn across the 
breadth of the white, the black will be positively and 
the white negatively electric when separate. Elec- 
tricity may be transferred from one body to another in 
the same manner as heat is communicated, and like it 
too, the body loses by the transmission. Although' no 
substance is altogether impervious to the electric fluid, 
nor is there any that does not oppose some resistance 
to its passage, yet it moves with much more facility 
through a certain class of substances called conductors, 
such as metals, water, the human body, &c., than 
through atmospheric air, glass, silk, &c., which are 
therefore called non-conductors. The conducing power 
is affected both by temperature and moisture.^ 

Bodies surrounded with non-conductors are said to be 
insulated, because, when charged, the electricity cannot 
escape. When that is not the case, the electricity is 
conveyed to the earth, which is formed of conducting 
matter; consequently it is impossible to accumulate 
electricity in a conducting substance that is not insu- 
lated. There are a great many substances called non- 
electrics, in which electricity is not sensibly developed 
by friction, unless they be insulated, probably because it 
is carried off by their conducting power as soon as 
elicited. Metals, for example, which are said to be 
18 



274 ELECTRICAL FORCES. SECT. XXVIII. 

non-electrics, can be excited, but being conductors, they 
cannot retain this state if in communication with the 
earth. It is probable that no bodies exist which are 
either perfect non-electrics or perfect non-conductors. 
But it is evident that electrics must be non-conductors 
to a certain degree, otherwise they could not retain 
their electric state. 

It has been supposed that an insulated body remains 
at rest, because the tension of the electricity, or its pres- 
sure on the air which restrains it, is equal on all sides ; 
but when a body in a similar state, and charged with 
the same kind of electricity, approaches it, that the mu- 
tual repulsion of the particles of the electric fluid di- 
minishes the pressure of the fluid on the air on the 
adjacent sides of the two bodies, and increases it on 
their remote ends ; consequently that equilibrium will 
be destroyed, and the bodies, yielding to the action of 
the preponderating force, will recede from or repel 
each other. When, on the contrary, they are charged 
with opposite electricities, it is alleged that the pressure 
upon the air on the adjacent sides will be increased by 
the mutual attraction of the particles of the electric 
fluid, and that on the further sides diminished ; con- 
sequently, that the force will urge the bodies toward 
one another, the motion in both cases corresponding to 
the forces producing it. An attempt has thus been 
made to attribute electrical attractions and repulsions to 
the mechanical pressure of the atmosphere. It is more 
than doubtful, however, whether these phenomena can 
be referijgpl to that cause ; but certain it is, that what- 
ever theTiature of these forces may be, they are not 
impeded in their action by the intervention of any sub- 
stance whatever, provided it be not itself in an electric 
state. 

A body charged with electricity, although perfectly 
insulated, so that all escape of electricity is precluded, 
tends to produce an electric state of the opposite kind 
in all bodies in its vicinity. Positive electricity tends 
to produce negative electricity in a body near to it, and 
vice versa, the effect being greater as the distance di- 
minishes. This power which electricity possesses, of 
causing an opposite electrical state in its vicinity, is called 



Scr. XXVllf. ELECTRICAL FORCES. 275 

induction. When a body in either electric state is pre- 
sented to a neutral one, its tendency, in consequence of 
the- law of induction, is to disturb the electrical condi- 
tion of the neutral body. The electrified body induces 
electricity contrary to its own in the adjacent part of 
the neutral one, and therefore an electrical state similar 
to its own in the remote part. Hence the neutrality of 
the second body is destroyed by the action of the first, 
and the adjacent parts of the two, having now opposite 
electricities, will attract each other. The attraction be- 
tween electrified and unelectrified substances is, there- 
fore, merely a consequence of their altered state, re- 
sulting directly from the law of induction, and not an 
original law. The effects of induction depend upon the 
facility with which the equilibrium of the neutral state 
of a body can be overcome a facility which is propor- 
tional to the conducting power of the body. Conse- 
quently the attraction exerted by an electrified substance 
upon another substance previously neutral, will be much 
more energetic if the latter be a conductor than if it be 
a non-conductor. 

The law of electrical attraction and repulsion has 
been determined by suspending a needle of gum-lac 
horizontally by a silk fibre, the needle carrying at one 
end a piece of electrified gold-leaf. A globe in the same, 
or in the opposite electrical state, when presented to 
the gold leaf, will repel or attract it, and will therefore 
cause the needle to vibrate more or less rapidly accord- 
ing to the distance of the globe. A comparison of the 
number of oscillations performed in a given lime at dif- 
ferent distances, will determine the law of the variation 
of the electrical intensity, in the same manner that the 
force of gravitation is measured by the oscillations of 
the pendulum. Coulomb invented an instrument which 
balances the forces in question by the force of the tor- 
sion of a thread, which consequently measures their 
intensity ; and Mr. Snow Harris has recently construct- 
ed an instrument with which he has measured the 
intensity of the electrical force in terms of the weight 
requisite to balance it. By these methods it has been 
found that the intensity of the electrical attraction and 
repulsion varies inversely as the squares of the distances. 



276 ELECTRICAL INDUCTION. SECT. XXV11I. 

However, the law of the repulsive force is liable to great 
disturbance from inductive action, which Mr. Snow Har- 
ris has found to exist not only between a charged and 
neutral body, but also between bodies similarly charged, 
and that in the latter case the inductive process may be- 
indefinitely modified by the various circumstances of the 
quantity and intensity of the electricity, and the distance 
between the charged bodies. Since electricity can only 
be in equilibrio from the mutual repulsion of its par- 
ticles, which according to these experiments varies in- 
versely as the square of the distances, its distribution in 
different bodies depends upon the laws of mechanics, 
and therefore becomes a subject of analysis and calcula- 
tion. Although the distribution of the electric fluid has 
employed the eminent analytical talents of M. Poisson 
and Mr. Ivory, and though many of their computed 
phenomena have been confirmed by observation, yet 
recent experiments show that the subject is still involved 
in much difficulty. Electricity is entirely confined to 
the surface of bodies ; or if it does penetrate their sub- 
stance, the depth is inappreciable ; so that the quantity 
bodies are capable of receiving does not follow the pro- 
portion of their bulk, but depends principally upon the 
form and extent of surface over which it is spread : thus 
the exterior may be positively or negatively electric, 
while the interior is in a state of perfect neutrality. 

It appears from the experiments of Mr. Snow Harris, 
that a given quantity of electricity divided between two 
perfectly equal and similar bodies, exerts upon external 
bodies only one-fourth of the attractive force apparent 
when disposed upon one of them ; and if it be distrib- 
uted among three equal and similar bodies, the force is 
one-ninth of that apparent when it is disposed on one of 
them. Hence if the quantity of electricity be the same, 
the force varies inversely as the square of the surface 
over which it is disposed ; and if the surface be the same, 
the force varies directly as the square of the quantity 
of the electric fluid. These laws however do not hold 
when the form of the surface is changed. A given 
quantity of electricity disposed on a given surface has the 
greatest intensity when the surface has a circular form, 
and the least intensity when the surface is expanded 



Scr. XXVIII. ELECTRICAL INTENSITY. 277 

into an indefinite right line. The decrease of intensity 
seems to arise from some peculiar arrangement of the 
electricity depending on the extension of the surface, 
and has been considered by Volta to consist in the re- 
moval of the electrical particles farther without the 
sphere of each other's influence. It i's quite independ- 
ent of the extent of the edge, the area being the same ; 
for Mr. Snow Hams found that the electrical intensity 
of a charged sphere is the same with that of a plane 
circular area of the same superficial extent, and that of 
a charged cylinder the same as if it were cut open and 
expanded into a plane surface. 

The same able electrician has shown that the attract- 
ive force between an electrified and a neutral uninsulated 
body is the same, whatever be the forms of their unop- 
posed parts. Thus two hemispheres attract each other 
with precisely the same force as if they were spheres ; 
and as the force is as the number of attracting points in 
operation directly, and as the squares of the respective 
distances inversely, it follows that the attraction between 
a mere ring and a circular area is no greater than that 
between two similar rings, and the force between a 
sphere and an opposed spherical segment of the same 
curvature is no greater than that of two similar segments, 
each equal to the given segment. 

Electricity may be accumulated to a great extent in 
insulated bodies : and so long as it is quiescent, it occa- 
sions no sensible change in their properties, though it is 
spread over their surfaces in indefinitely thin layers. 
When restrained by the non-conducting power of the 
atmosphere, the tension or pressure exerted by the elec- 
tric fluid against the air which opposes its escape, is in 
the ratio compounded of the repulsive force of its own 
particles at the surface of the stratum of the fluid, and 
of the thickness of that stratum. But as one of these 
elements is always proportional to the other, the total 
pressure on eveiy point must be proportional to the 
squares of the thickness. 'If this pressure be less than 
the coercive force of the ah*, the electricity is retained ; 
but the instant it exceeds that force in any one point, 
the electricity escapes, which it will do when the air is 
attenuated, or becomes saturated with moisture. ' Tt ap- 
A A 



278 ELECTRICAL INTENSITY. SECT. XXVIII. 

pears that the resistance of the air to the passage of the 
electric fluid is proportional to the square of its density, 
but that the action of electricity on distant bodies by in- 
duction is quite independent of atmospheric pressure, 
and is the same in vacuo as in air. 

The power of retaining electricity depends also upon 
the shape of the body. It is most easily retained by a 
sphere, next to that by a spheroid, but it readily escapes 
from a point; and a pointed object receives it with 
most facility. It appears from analysis, that electricity, 
when in equilibrio, spreads itself in a thin stratum over 
the surface of a sphere, in consequence of the repulsion 
of its particles, which force is directed from the center 
to the surface. In an oblong spheroid, the intensity or 
thickness of the stratum of electricity at the extremities 
of the two axes is exactly in the proportion of the axes 
themselves ; hence, when the ellipsoid is much elon- 
gated, the electricity becomes very feeble at the equator, 
and powerful at the poles. A still greater difference in 
the intensities takes place in bodies of cylindrical or 
prismatic form, and the more so in proportion as their 
length exceeds their breadth ; therefore the electrical 
intensity is very powerful at a point where nearly the 
whole electricity in the body is concentrated. Not- 
withstanding these analytical results, it is doubted 
whether the disposition of electrified bodies to discharge 
their electricity from points or edges may not arise from 
the superior attractive force generated by induction in 
external bodies, rather than from an original concentra- 
tion of the electric fluid in these parts. 

A perfect conductor is not mechanically affected by 
the passage of electricity, if it be of sufficient size to 
carry off the whole ; but it is shivered to pieces in an 
instant if it be too small to carry off the charge : this 
also happens to a bad conductor. In that case the 
physical change is generally a separation of the particles, 
though it may occasionally be attributed to chemical 
action, or expansion from the heat evolved during the 
passage of the fluid ; but all these effects are in propor- 
tion to the obstacles opposed to the freedom of its 
course. The heat produced by the electric shock is 
intense, fusing metals, and even volatilizing substances, 



Ill 

,: 

to 



SECT. XXVIII. ELECTRICAL LIGHT. 279 

though it is only accompanied by light when the fluid is 
obstructed in its passage. 

Electrical light, when analyzed by the prism, pre- 
sents very different appearances to the solar light. 
Frauenhofer found that instead of the fixed dark lines 
of the solar spectrum, the spectrum of an electric spark 
was crossed by very numerous bright lines ; and Pro- 
fessor Wheatstone has observed that the number and 
position of the lines differ with the metal from which 
the spark is taken. According to M. Biot, electrical 
light arises from the condensation of the air during the 
rapid motion of the electricity r and varies both in in- 
tensity and color with the density of the atmosphere. 
When the air is dense, it is white and brilliant; whereas 
in rarefied air it is diffuse and of a reddish color. The 
experiments of Sir Humphiy Davy, however, seem to 
be at variance with this opinion. He passed the elec- 
tric spark through a vacuum over mercury, which, 
from green, became successively sea-green, blue, and 
purple, on admitting different quantities of air. When 
the vacuum was made over a fusible alloy of tin and 
bismuth, the spark was yellowish and extremely pale. 
Sir Humphry thence concluded, that electrical light 
principally depends upon some properties belonging to 
the ponderable matter through which it passes, and 
that space is capable of exhibiting luminous appearances, 
though it does not contain an appreciable quantity of 
this matter. He thought it not improbable that the 
superficial particles of bodies which form vapor, when 
detached by the repulsive power of heat, might be 
equally separated by the electric forces, and produce 
luminous appearances in vacuo, by the destruction of 
their opposite electric states. Professor Wheatstone 
has been led to conclude that electrical light results 
from the volatilization and ignition of the ponderable 
matter of the conductor itself. 

Pressure is a source of electricity which M. Becquerel 
has found to be common to all bodies ; but it is necessary 
to insulate them to prevent its escape. J When two sub- 
stances of any kind whatever are insulated and pressed 
together, they assume different electric states, but they 
only show contrary electricities when one of them is a 



280 SOURCES OF ELECTRICITY. SECT. XXVIII. 

good conductor. When both are good conductors, they 
must be separated with extreme rapidity, to prevent 
the return to equilibrium. /When the separation is 
very sudden, the tension of the two electricities may be 
great enough to produce light. ; M. Becquerel attributes 
the light produced by the collision of icebergs to this 
cause. Iceland spar is made electric by the smallest 
pressure between the finger and thumb, and retains it 
for a long time. All these circumstances are modified 
by the temperature of the substances, the state of their 
surfaces, and that of the atmosphere. Several crys- 
taline substances become electric when heated, es- 
pecially tourmaline, one end of which acquires positive 
and the other negative electricity, while the interme- 
diate partis neutral. If a tourmaline be broken through 
the middle, each fragment is found to possess positive 
electricity at one encH and negative at the other, like 
the entire crystal. Electricity is evolved by bodies 
passing from a liquid to a solid state ; also by chemical 
action during the production and condensation of vapor, 
which is consequently a great source of atmospheric 
electricity. The steam issuing from the valve of an 
insulated locomotive steam engine produces seven times 
the quantity of electricity that an electrifying machine 
would do with a plate three feet in diameter, and 
worked at the rate of 70 revolutions in a minute.) In 
short, it may be stated generally, that when any <4use 
whatever, such as friction, pressure, heat, fracture, 
chemical action, &c., tends to destroy molecular attrac- 
tion, there is a development of electricity. If, however, 
the molecules be not immediately separated, there will 
be an instantaneous restoration of equilibrium. 

The earth possesses a powerful electrical tension, and 
the atmosphere, when clear, is almost always positively 
electric. Its electricity is stronger in winter than in 
summer, during the day than in the night. The inten- 
sity increases for two or three hours from the time of 
sunrise, comes to a maximum between seven and eight, 
then decreases toward the middle of the day, arrives at 
its minimum between one and two, and again augments 
as the sun declines, till about the time of sunset, after 
which it diminishes, and continues feeble during the 



SKCT. XXVni. ATMOSPHERIC ELECTRICITY. 281 

night,/ Atmospheric electricity arises partly from an 
evolution of the electric fluid during the evaporation 
that is so abundant at the surface of the earth, though 
not under all circumstances. M. Pouillet has recently 
come to the conclusion, that simple evaporation never 
produces electricity, unless accompanied by chemical 
action, but that electricity is always disengaged when 
the water holds a salt or some other substance in solu- 
tion, f He found when water contains lime, chalk, or 
any solid alkali, that the vapor arising from it is nega- 
tively electric ; and when the body held in solution is 
either gas, acid, or some of the salts, that the vapor 
given out is positively electric. / The ocean must there- 
fore afford a great supply of"positive electricity to the 
atmosphere ; but as M. Becquerel has shown that elec- 
tricity of one kind or other is developed, whenever the 
molecules of bodies are deranged from their natural 
positions of equilibrium by any cause whatever, the 
chemical changes on the surface of the globe must occa- 
sion many variations in the electrical state of the atmos- 
phere. 

Clouds probably owe their existence, or at least their 
form, to electricity, for according to some authors they 
consist of hollow vesicles of vapor coated with it. As 
the electricity is either entirely positive or negative, the 
vesicles repel each other, which prevents them from 
uniting and falling down in rain. The friction of the 
surfaces of two gjrata of air moving in different direc- 
tions, probably developes electricity; and if the strata 
be of different temperatures, a portion of the vapor they 
always contain will be deposited ; the electricity evolved 
will be 'taken up by the vapor, and cause it to assume 
the vesicular state constituting a cloud. A vast deal of 
electricity may be accumulated in this manner, which 
may be either positive or negative. When two clouds, 
charged with opposite kinds, approach within a certain 
distance, the thickness of the coating of electricity in- 
creases on the two sides of the clouds that are nearest 
to one another; and when the accumulation becomes 
so great as to overcome the coercive pressure of the 
atmosphere, a discharge takes place, which occasions a 
flash of lightning. The actual quantity of electricity in 

AA2 



282 ELECTRIC CLOUDS. . SECT. XXVIII. 

any one part of a cloud is extremely small. The inten- 
sity of the flash arises from the very great extent of 
surface occupied by the electricity; so that clouds may 
be compared to enormous Leyden jars thinly coated 
with the electric fluid, which only acquires its intensity 
by its instantaneous condensation. The rapid and irreg- 
ular motions of thunder clouds are, in all probability, 
more owing to strong electrical attractions and repul- 
sions among themselves than to currents of air, though 
both are no doubt concerned in these hostile move- 
ments. 

Since the air is a non-conductor, it does not convey 
the electricity from the clouds to the earth, but it ac- 
quires from them an opposite electricity, and when the 
tension is very great the force of the electricity becomes 
irresistible, and an interchange takes place between the 
clouds and the earth ; but so rapid is the motion of light- 
ning, that it is difficult to ascertain when it goes from the 
clouds to the earth, or shoots upward from the earth 
to the clouds, though there can be no doubt that it does 
both. In a storm which occurred at Manchester, in the 
month of June, 1835, the electric fluid was observed to 
issue from various points of a road, attended by explo- 
sions as if pistols had been fired out of the ground. A 
man appears to have been killed by one of these explo- 
sions taking place under his right foot. M. Gay-Lussac 
has ascertained that a flash of lightning sometimes darts 
more than three miles at once in a straight line. 

A person may be killed by lightning, although the 
explosion takes place at the distance of twenty miles, 
by what is called the back stroke. Suppose that the 
two extremities of a cloud highly charged with electri- 
city hang down toward the earth : they will repel the 
electricity from the earth's surface, if it be of the same 
kind with their own, and will attract the other kind ; 
and if a discharge should suddenly take place at one 
end of the cloud, the equilibrium will instantly be re- 
stored by a flash at that point of the earth which is un- 
der the other. Though the back stroke is often suffi- 
ciently powerful to destroy life, it is never so terrible in 
its effects as the direct shock, which is frequently of 
inconceivable intensity- Instances have occurred in 



SECT. XXVIII. LIGHTNING CONDUCTORS. 283 

which large masses of iron and stone, and even many 
feet of a stone wall, have been conveyed to a con- 
siderable distance by a stroke of lightning. Rocks and 
the tops of mountains often bear the marks of fusion 
from its action; and occasionally vitreous tubes, de- 
scending many feet into banks of sand, mark the path 
of the electric fluid. Some years ago, Dr. Fiedler ex- 
hibited several of these fulgorites in London, of con- 
siderable length, which had been dug out of the sandy 
plains of Silesia and Eastern Prussia. One found at 
Paderborn was forty feet long. Their ramifications 
generally terminate in pools or springs of water below 
the sand, which are supposed to determine the course 
of the electric fluid. No doubt the soil and substrata 
must influence its direction, since it is found by experi- 
ence that places which have been struck by lightning 
are often struck again. A school-house in Lammer- 
muir, East Lothian, has been struck three different 
times. 

The atmosphere, at all times positively electric, be- 
comes intensely so on the approach of rain, snow, wind, 
hail, or sleet ; but it afterward varies, and the transi- 
tions are very rapid on the approach of a thunder-storm. 
An isolated conductor then gives out such quantities of 
sparks that it is dangerous to approach it, as was fatally 
experienced by Professor Richman, at Petersburg, who 
was struck dead by a globe of fire from the extremity 
of a conductor, while making experiments on atmos- 
pheric electricity. There is no instance on record of an 
electric cloud of high tension being dispelled by a con- 
ducting rod silently withdrawing the electric fluid ; yet 
it may mitigate the stroke, or render it harmless if it 
should come. Copper conductors afford the best pro- 
tection against lightning, especially if they expose a 
broad surface, since the electric fluid is conveyed along 
the exterior of bodies. Conductors do not attract the 
electric fluid from the clouds ; their object is to carry 
it off in case of a stroke, and therefore they ought to 
project very little, if at all, above the building. 

When the air is highly rarefied by heat, its coercive 
power is diminished so that the electric fluid escapes 
from the clouds, and never can be accumulated beyond 



284 VELOCITY OF ELECTRICITY. SECT. XXVIII. 

a certain limit; whence those lambent diffuse flashes of 
lightning without thunder so frequent in warm summer 
evenings." 

The velocity of electricity is so great, that the most 
rapid motion which can be produced by art appears to 
be actual rest when compared with it. A wheel re- 
, volving with celerity sufficient to render its spokes invis- 
\ ible, when illuminated by a flash of lightning, is seen for 
: an instant with all its spokes distinct, as if it were in a 
state of absolute repose ; because, however rapid the 
\ rotation may be, the light has come and already ceased 
before the wheel has had time to turn through a sensible 
space. This beautiful experiment is due to Professor 
Wheatstone, as well as the following variation of it, 
which is not less striking : Since a sunbeam consists of 
a mixture of blue, yellow, and red light, if a circular 
piece of pasteboard be divided into three sectors, one of 
which is painted blue, another yellow, and a third red, 
it will appear to be white when revolving quickly, be- 
cause of the rapidity with which the impressions of the 
colors succeed each other on the retina. But the in- 
stant it is illuminated by an electric spark, it seems to 
stand still, and each color is as distinct as if it were at 
rest. This transcendent speed of the electric fluid has 
been ingeniously measured by Professor Wheatstone ; 
and although his experiments are not far enough ad- 
vanced to enable him to state its absolute celerity, he has 
ascertained that it much surpasses the velocity of light. 
In the horizontal diameter of a small disc fixed on the 
wall of a darkened room are disposed six small brass 
balls, well insulated from each other. An insulated 
copper wire half a mile long is disjoined in its middle, 
and also near its two extremities ; the six ends thus ob- 
tained are connected with the six balls on the disc. 
When an electric discharge is sent through the wire by 
connecting its two extremities, one with the positive, 
and the other with the negative coating of a Leyden 
jar, three sparks are seen on the disc, apparently at the 
same instant. At the distance of about ten feet, a small 
revolving mirror is placed so as to reflect these three 
sparks during its revolution. From the extreme velocity 
of the electricity, it is clear, that if the three sparks bo 



SECT. XXVIII. VELOCITY OF ELECTRICITY. 285 

simultaneous, they will be reflected, and will vanish be- 
fore the mirror has sensibly changed its position, how- 
ever rapid its rotation may be, and they will be seen in a 
straight line. But if the three sparks be not simultane- 
ously transmitted to the disc if one, for example, be later 
than the other two- the mirror will have time to revolve 
through an indefinitely small arc in the interval between 
the reflection of the two sparks and that of the single 
one. However, the only indication of this small motion 
of the mirror will be, that the single spark will not be 
reflected in the same straight line with the other two, 
but a little above or below it, for the reflection of all 
three will still be, apparently simultaneous, the time in- 
tervening being much too short to be appreciated. 

Since the number of revolutions which the revolving 
mirror makes in a second are known, and the angular 
deviation of the reflection of the single spark from the 
reflection of the other two can be measured, the time 
elapsed between their consecutive reflections can be as- 
certained. And as the length of that part of the wire 
through which the electricity has passed is given, its ve- 
locity may be found. 

Since the number of pulses in a second requisite to 
produce a musical note of any pitch is known, the num- 
ber of revolutions accomplished by the mirror in a given 
time may be determined from the musical note produced 
by a tooth or peg in its axis of rotation striking against a 
card, or from the notes of a siren attached to the axis. 
It was thus that Professor Wheatstone found the mir- 
ror which he employed in his experiments to make 800 
revolutions in a second; and as the angular velocity of 
the reflected image in a revolving mirror is double that 
of the mirror itself, an angular deviation of one degree 
in the appearance of the two sparks would indicate an 
interval of the 576,000th of a second ; the deviation of 
half 'a degree would, therefore, indicate more than the 
millionth of a second. The use of sound as a measure 
of velocity is a happy illustration of the connection of the 
physical sciences. 

When the atmosphere is highly charged with elec- 
tricity, it not unfrequentiy happens that electric light in 
the form of a star is seen on the topmast and yard-arms 



286 PHOSPHORESCENCE. SECT. XXVm. 

of ships. In 1831 the French officers at Algiers were 
surprised to see brushes of light on the heads of their 
comrades, and at the points of their fingers, when they 
held up their hands. This phenomenon was well known 
to the ancients, who reckoned it a lucky omen. 

Many substances in decaying emit light, which is at- 
tributed to electricity, such as fish and rotten wood. 
Oyster shells, and a variety of minerals, become phos- 
phorescent at certain temperatures, when exposed to 
electric shocks or friction : indeed most of the causes 
which disturb molecular equilibrium give rise to phos- 
phoric phenomena. The minerals possessing this prop- 
erty are generally colored or imperfectly transparent ; 
and though the color of this light varies in different sub- 
stances, it has no fixed relation to the color of the min- 
eral. An intense heat entirely destroys this property, 
and the phosphorescent light developed by heat has no 
connection with light produced by friction, for Sir David 
Brewster observed that bodies deprived of the faculty of 
emitting the one are still capable of giving out the other. 
Among the bodies which generally become phosphores- 
cent when exposed to heat, there are some specimens 
which do not possess this property, wherefore phospho- 
rescence cannot be regarded as an essential character of 
the minerals possessing it. Sulphuret of calcium, known 
as Canton's phosphorus, and the sulphuret of barium, or 
Bologna stone, possess the phosphorescent property in 
an eminent degree, and M. Edmond Becquerel has shown 
that on these substances a very remarkable phosphores- 
cent effect is produced by the action of the different 
rays of the solar spectrum. In former times Beccaria 
stated that the violet ray was the most energetic, and 
the red ray the least so, in exciting phosphoric light. M. 
Becquerel has shown that two luminous bands separated 
by a dark one are excited by the solar spectrum on pa- 
per covered with a solution of gum-arabic and strewed 
with powdered sulphuret of calcium. One of the lu- 
minous bands occupies the space under the least refran- 
gible violet rays, and the other that beyond the lavender 
rays, so that the dark band lies on the part under the 
extreme violet and lavender rays. When the action of 
the spectral light is continued, the whole surface beyond 



SJBCT. XXVIII. PHOSPHORESCENCE. 287 

the least refrangible violet shines, the luminous bands 
already mentioned brightest, but all the space from the 
least refrangible violet to the extreme red remains dark. 
If the surface prepared with either the sulphuret of cal- 
cium or the Bologna stone be exposed to the sun's light 
for a short time it becomes luminous all over, but when 
in this state a solar spectrum is thrown upon it, the 
whole remains luminous except the part from the least 
refrangible violet to the extreme red, on which space 
the light is extinguished ; and when the temperature of 
this surface is raised by a lamp, the bright parts become 
more luminous and the dark parts remain dark. Glass 
stained by the protoxide of copper, which transmits only 
the red and orange rays together with the chemical rays 
that accompany them, has ^he same effect with the less 
refrangible part of the spectrum ; hence there can be no 
doubt that the most refrangible and obscure rays of the 
spectrum excite phosphorescence, while all the less re- 
frangible rays of light and heat extinguish it. It appears 
from the experiments of MM. Biot and Becquerel that 
electrical disturbance produces these phosphorescent 
effects. There is thus a mysterious connection between 
the most refrangible rays and electricity, which the ex- 
periments of iVI. E. Becquerel confirm, showing that 
electricity is developed during chemical action by the 
violet rays, that it is very feebly developed by the blue 
and indigo, but that none is excited by the less refrangi- 
ble part of the spectrum. 

Paper prepared with the sulphuret of barium when 
under the solar spectrum shows only one space of max- 
imum luminous intensity, and the destroying rays are 
the same as in sulphuret of calcium. 

Thus the obscure rays beyond the extreme violet 
possess the property of producing light, while the lumi- 
nous rays have the power of extinguishing it. 

The phosphoric spectrum has inactive lines which 
coincide with those in the luminous and chemical spec- 
tra at least as far as it extends, but in order to be seen, 
the spectrum must be received for a few seconds upon 
the prepared surface through, an aperture in a dark 
room, then the aperture must be closed, and the tem- 
perature of the surface raised two or three hundred 



288 PHOSPHORESCENCE. SECT. XXVIII. 

degrees ; the phosphorescent parts then shine brilliantly, 
and the dark lines appear black. 

Since the parts of similar refrangibility in the differ- 
ent spectra are traversed by the same dark lines, rays 
of the same refrangibility are probably absorbed at the 
same time by the different media through which they 
pass. Multitudes of fish are endowed with the power 
of emitting light at pleasure, no doubt to enable them 
to pursue their prey at depths where the sunbeams can- 
not penetrate. Flashes of light are frequently seen to 
dart along a shoal of herrings or pilchards ; and the 
Medusa tribes are noted for their phosphorescent brill- 
iancy, many of which are extremely small, and so nu- 
merous as to make the wake of a vessel look like a stream 
of silver. Nevertheless, the luminous appearance which 
is frequently observed in the sea during the summer 
months cannot always be attributed to marine animalcule, 
as the following narrative will show : 

Captain Bonnycastle, coming up the Gulf of St. Law- 
rence on the 7th of September, 1826, was roused by 
the mate of the vessel in great alarm from an unusual 
appearance. It was a starlight night, when suddenly 
the sky became overcast in the direction of the high 
land of Cornwallis country, and an instantaneous and 
intensely vivid light, resembling the aurora, shot out of 
the hitherto gloomy and dark sea on the lee bow, which 
was so brilliant that it lighted everything distinctly, even 
to the mast-head. The light spread over the whole 
sea between the two shores, and the waves, which be- 
fore had been tranquil, now began to be agitated. Cap- 
tain Bonnycastle describes the scene as that of a blazing 
sheet of awful and most brilliant light. A long and vivid 
line of light, superior in brightness to ,the parts of the 
sea not immediately near the vessel, showed the base 
of the high, frowning, and dark land abreast : the sky 
became lowering and more intensely obscure. Long, 
tortuous lines of light showed immense numbers of very 
large fish darting about as if in consternation. The 
spritsail-yard and mizen-boom were lighted by the glare, 
as if gas-lights had been r burning directly below them ; 
and until just before dayoreak, at four o'clock, the most 
minute objects were distinctly visible. Day broke very 



SECT. XXVIII. AURORA BOREALIS. 289 

slowly, and the sun rose of a fiery and threatening as- 
pect. Rain followed. Captain Bonnycastle caused a 
bucket of this fiery water to be drawn up ; it was one 
mass of light when stirred by the hand, and not in sparks 
as usual, but in actual coruscations. A portion of the 
water preserved its luminosity for seven nights. On 
the third night, .the scintillations of the sea reappeared ; 
this evening the sun went down very singularly, exhibit- 
ing in its descent a double sun ; and when only a few 
degrees high, its spherical figure changed into that of 
a long cylinder, which reached the horizon. In the 
night the sea became nearly as luminous as before, but 
on the fifth night the appearance entirely ceased. Cap- 
tain Bonnycastle does not think it proceeded from ani- 
malculae, but imagines it might be some compound of 
phosphorus, suddenly evolved and disposed over the sur- 
face of the sea ; perhaps from the exuviae or secretions 
of fish connected with the oceanic salts, muriate of soda, 

a-,nd sulphate of magnesia. 

The aurora borealis is decidedly an electrical phenom- 
enon, which takes place in the highest regions of the 
atmosphere, since it is visible at the same time from 
places very far distant from each other. It is somehow 
connected with the magnetic poles of the earth, and oc- 
casions vibrations in the magnetic needle. M. Arago 
has frequently remarked that the needle was powerfully 
agitated at Paris, by an aurora that was below the hori- 
zon, and consequently invisible, but whose existence 
was known from the observations of the polar navigators. , 
The aurora has never been seen so far north as the pole 
of the earth's rotation, nor does it extend to low latitudes. 
It generally appears in the form of a luminous arch, 
stretching more or less from east to west, but never from 
north to south, the most elevated point being always in 
the magnetic meridian of the place of the observer ; and 
across the arch the coruscations are rapid, vivid, and of 
various colors, but whether there be any sound is still a 
disputed point. A similar phenomenon occurs in the high 
latitudes of the southern hemisphere. Dr. Faraday- 
conjectures that the electric equilibrium of the earth is 
restored by the aurora conveying the electricity from the 
poles to the equator. 

19 BB 



290 VOLTAIC ELECTRICITY. SECT. XXIX. 



SECTION XXIX. 

Voltaic Electricity The Voltaic Battery Intensity Quantity Compari- 
son of the Electricity of Tension with Electricity in Motion Luminous 
Effects Decomposition of Water Formation of. Crystals by Voltaic 
Electricity Electrical Fish. 

VOLTAIC electricity is of that peculiar kind which is 
elicited by the force of chemical action. It is connected 
with one of the most brilliant periods of British science, 
from the splendid discoveries to which it led Sir Hum- 
phry Davy ; and it has acquired additional interest 
since the discovery of the reciprocal action of Voltaic 
and magnetic currents, which has proved that magnetism 
is only an effect of electricity, and that it has no existence 
as a distinct or separate principle. Consequently Voltaic 
electricity, as immediately connected with the theory of 
the earth and planets, forms a part of the physical ac- 
count of their nature. 

In 1790, while Galvani, Professor of Anatomy in Bo- 
logna, was making experiments on electricity, he was 
surprised to see convulsive motions in the limbs of a 
dead frog accidentally lying near the machine during an 
electrical discharge. Though a similar action had been 
noticed long before his time, he was so much struck with 
this singular phenomenon, that he examined all the cir- 
cumstances carefully, and at length found that convulsions 
take place when the nerve and muscle of a frog are con- 
nected by a metallic conductor. This excited the atten- 
tion of all Europe ; and it was not long before Professor 
Volta of Pavia showed that the mere contact of different 
bodies is sufficient to disturb electrical equilibrium, and 
that a current of electricity flows in one direction through 
a circuit of three conducting substances. From this he 
was led, by acute reasoning and experiment, to the con- 
struction of the Voltaic pile, which, in its early form, 
consisted of alternate discs of zinc and copper, separated 
by pieces of wet cloth, the extremities being connected 
by wires. This simple apparatus, perhaps the most 
wonderful instrument that has been invented by the in- 
genuity of man, by divesting electricity of its sudden and 



SECT. XXIX. THE VOLTAIC BATTERY. 291 

uncontrollable violence, and giving in a continued stream 
a greater quantity at a diminished intensity, has exhibited 
that fluid under a new and manageable form, possessing 
powers the most astonishing and unexpected. As the 
Voltaic batteiy has become one of the most important 
engines of physical research, some account of its present 
condition may not be out of place.) 

The disturbance of electric equilibrium, and a devel- 
opment of electricity, invariably accompany the chem- 
ical action of the fluid on metallic substances, and are 
most plentiful when that action occasions oxidation. 
Metals vary in the quantity of electricity afforded by 
their combination with oxygen. But the greatest 
abundance is developed by the oxidation of zinc by weak 
sulphuric acid. [And in conformity with the law that 
one kind of electricity cannot be evolved without an 
equal quantity of the other being brought into activity, 
it is found that the acid is positively, and the zinc nega- 
tively electric. It has not yet been ascertained why 
equilibrium is not restored by the contact of these two 
substances, which are both conductors, and in opposite 
electrical states. However, the electrical and chemical 
changes are so connected, that unless equilibrium be 
restored, the action of the acid will go on languidly, or 
stop as soon as a certain quantity of electricity is accu- 
mulated in it. Equilibrium nevertheless will be restored, 
and the action of the acid will be continuous, if a plate of 
copper be placed in contact with the zinc, both being 
immersed in the fluid ; for the copper, not being acted 
upon by the acid, will serve as a conductor to convey 
the positive electricity from the acid to the zinc, and 
will at every instant restore the equilibrium, and then 
the oxidation of the zinc will go on rapidly. (Thus 
three substances are concerned in forming a voltaic 
circuit, but it is indispensable that one of them should 
be a fluid, j The electricity so obtained will be very 
feeble in overcoming resistances offered by imperfect 
conductors interposed in the circuit, or by very long 
wires, but it may be augmented by increasing the num- 
ber of plates. In the common Voltaic battery, the 
electricity which the fluid has acquired from the first 
plate of zinc, exposed to its action, is taken up by the 



292 THE VOLTAIC BATTERY. SECT. XXIX. 

copper plate belonging to the second pair, and transferred 
to the second zinc plate, with which it is connected. 
The second plate of zinc possessing equal powers, and 
acting in conformity with the first, having thus acquired 
a larger portion of electricity than its natural share, 
communicates a larger quantity to the fluid in the second 
cell. This increased quantity is again transferred to 
the next pair of plates ; and thus every succeeding al- 
ternation is productive of a further increase in the 
quantity of the electricity developed. This action, 
however, would stop unless a vent were given to the 
accumulated electricity, by establishing a communication 
between the positive and negative poles of the battery, 
by means of wires attached to the extreme plate at each 
end. When the wires are brought into contact, the 
Voltaic circuit is completed, the electricities meet and 
neutralize each other, producing the shock and other 
electrical phenomena ; and then the electric current 
continues to flow uninterruptedly in the circuit, as long 
as the chemical action lasts. The stream of positive 
electricity flows from the zinc to the copper. The 
construction and power of the Voltaic battery has been 
much improved of late years, but the most valuable 
recent improvement is the constant battery of Professor 
Daniell. In all batteries of the ordinary construction, 
the power, however energetic at first, rapidly diminishes, 
and ultimately becomes very feeble. Professor Daniell 
found that this diminution of power is occasioned by the 
adhesion of the evolved hydrogen to the surface of the 
copper, and to the precipitation of the sulphate formed 
by the action of the acid on the zinc. He prevents the 
latter by interposing between the copper and the zinc, 
in the cell containing the liquid, a membrane which, 
without impeding the electric current, prevents the 
transfer of the salt; and the former, by placing between 
the copper and the membrane solution of sulphate of 
copper, which being reduced by the hydrogen prevents 
the adhesion of this gas to the metallic surface. Each 
element of the battery consists of a hollow cylinder of 
copper, in the axis of which is placed a cylindrical rod of 
zinc ; between the zinc and the copper a membranous 
bag is placed, which divides the cell into two portions, 



SKCT. XXIX. THE VOLTAIC BATTERY. 293 

the inner of which is filled with dilute acid, and the one 
nearer the copper is supplied with crystals of the sul- 
phate of that metal. The battery consists of several of 
these elementary cells connected together by metallic 
wires, the zinc rod of one with the copper cylinder of 
that next to it. The zinc rods are amalgamated, so that 
local action, which in ordinaiy cases is so destructive of 
the zinc, does not take place, and no chemical action is 
manifested unless the circuit be completed. The rods 
are easily detached, and others substituted for them 
when worn out. This battery, which possesses con- 
siderable power, and is constant in its effects for a very 
long period of time, is greatly superior to all former ar- 
rangements, either as an instrument of research, or for 
exhibiting the ordinaiy phenomena of Voltaic electricity. 

A battery charged with water alone, instead of acid, 
is very constant in its action, but the quantity of elec- 
tricity it developes is comparatively very small. Mr. 
Cross of Broomfield in Somersetshire, has kept a bat- 
tery of this kind in full force during twelve months. 
M. Becquerel had invented an instrument for comparing 
the intensities of the different kinds of electricity by 
means of weights,! but as it is impossible to make the 
comparison with Voltaic electricity produced by the or- 
dinary batteries, on account of the perpetual variation 
to which the intensity of the current is liable, he has 
constructed a battery which affords a continued stream 
of electricity of uniform power, but it is also of very 
feeble force. The current is produced by the chemical 
combination of an acid with an alkali. 

Metallic contact is not necessary for the production of 
Voltaic electricity, which is entirely due to chemical 
action. The intensity of the Voltaic electricity is in 
proportion to the intensity of the affinities concerned in 
its production, and the quantity produced is in propor- 
tion to the quantity of matter which has been chem- 
ically active during its evolution. Dr. Faraday considers 
this definite production to be one of the strongest proofs 
that the electricity is of chemical origin. 

Galvanic or Voltaic, like common electricity, may 
either be considered to consist of two fluids passing in 
opposite directions through the circuit, or, if the hypoth- 

B B2 



294 VOLTAIC ELECTRICITY. SECT. XXIX. 

esis of one fluid be adopted, the zinc end of the bat- 
tery may be supposed to have an excess of electricity, 
and the copper end a deficiency. Hence, in the latter 
case, the zinc is the positive end of the battery, and the 
copper the negative. 

Voltaic electricity is distinguished by two marked 
characters. Its intensity increases with the number of 
plates its quantity with the extent of their surfaces. 
The most intense concentration of force is displayed by 
a numerous series of large plates, light and heat are 
copiously evolved, and chemical decomposition is accom- 
plished with extraordinary energy ; whereas the elec- 
tricity from one pair of plates, whatever their size may 
be, is so feeble that it gives no sign either of attraction 
or repulsion ; and, even with a battery consisting of a 
very great number of plates, it is difficult to render the 
mutual attraction of its two wires sensible, though of 
opposite electricities. 

The action of Voltaic electricity differs in some re- 
spects materially from that of the ordinary kind. When 
a quantity of common electricity is accumulated, the 
restoration of equilibrium is attended by an instantaneous 
violent explosion, accompanied by the development of 
light, heat, and sound. The concentrated power of the 
fluid forces its way through every obstacle, disrupting 
and destroying the cohesion of the particles of the bodies 
through which it passes, and occasionally increasing its 
destructive effects by the conversion of fluids into steam 
from the intensity of the momentary heat, as when 
trees are torn to pieces by a stroke of lightning. Even 
the vivid light which marks the path of the electric fluid 
is probably owing in part to the sudden compression of 
the air and other particles of matter during the rapidity 
of its passage, or to the violent and abrupt reunion of 
the two fluids. But the instant equilibrium is restored 
by this energetic action the whole is a-t an end. On the 
contrary, when an accumulation takes place in a Voltaic 
battery, equilibrium is restored the moment the circuit 
is completed. But so far is the electric stream from 
being exhausted, that it continues to flow silently and 
invisibly in an uninterrupted current supplied by a per- 
petual reproduction. And although its action on bodies 



SCT. XXIX. VOLTAIC ELECTRICITY. 295 

is neither so sudden nor so intense as that of common 
electricity, yet it acquires such power from constant 
accumulation and continued action, that it ultimately 
surpasses the energy of the other. The two kinds of 
electricity differ in no circumstance more than in the 
development of heat. Instead of a momentary evolu- 
tion, which seems to arise from a forcible compression 
of the particles of matter during the passage of the com- 
mon electric fluid, the circulation of the Voltaic electricity 
is accompanied by a continued development of heat, 
lasting as long as the circuit is complete, without pro- 
ducing either light or sound ; and this appears to be its 
immediate direct effect, independent of mechanical ac- 
tion. Its intensity from a very powerful battery is 
greater than that of any heat that can be obtained by 
artificial means, so that it fuses substances which resist 
the action of the most powerful furnaces. The temper- 
ature of every part of a Voltaic battery itself is raised 
during its activity. 

When the battery is powerful, the luminous effects of 
Voltaic electricity are very brilliant. But considerable 
intensity is requisite to enable the electricity to force its 
way through the air on bringing the wires "together 
from the opposite poles. Its transit is accompanied by 
light ; and in consequence of the continuous supply of 
the fluid, sparks occur every time the contact of the 
wires is either broken or renewed. The most splendid 
artificial light known is produced by fixing pencils of 
charcoal at the extremities of the wires, and bringing 
them into contact. This light is the more remarkable, 
as it appears to be independent of combustion, since the 
charcoal suffers no change, and likewise because it is 
equally vivid in such gases as do not contain oxygen. 
Though nearly as bright as solar light, it differs materi- 
ally from it when analyzed with a prism. Professor 
Wheatstone has found that the appearance of the spec- 
trum of the Voltaic spark depends upon the metal from 
whence the spark is taken. The spectrum of that from 
mercury consists of seven definite rays, separated from 
each other by dark intervals ; these visible rays are two 
orange lines close together, a bright green line, two 
bluish green lines near each other, a very bright purple 



296 VOLTAIC ELECTRICITY. SECT. XXIX. 

line, and lastly a violet line. The spark taken from 
zinc, cadmium, tin, bismuth, and lead in the melted 
state, gives similar results ; but the number, position, 
and color of the lines vary so much in each case, and 
the appearances are so different, that the metals may be 
easily distinguished from each other by this mode of 
investigation. It appears, moreover, that the light does 
not arise from the combustion of the metal ; for the 
Voltaic spark taken from mercury successively in the 
vacuum of an air-pump, in the Torricellian vacuum, and 
in carbonic acid gas, is precisely the same as when the 
experiment is performed in the air or in oxygen gas. 
Notwithstanding the difference between electric and 
solar light, M. Arago is inclined to attribute the intense 
light and heat of the sun to electrical action. 

Voltaic electricity is a powerful agent in chemical 
analysis. When transmitted through conducting fluids 
it separates them into their constituent parts, which it 
conveys in an invisisible state through a considerable 
space or quantity of liquid to the poles, where they 
come into evidence. Numerous instances might be 
given, but the decomposition of water is perhaps the 
most simple and elegant. Suppose a glass tube filled 
with water and corked at both ends ; if one of the wires 
of an active Voltaic battery be made to pass through 
one cork and the other through the other cork, into the 
water, so that the extremities of the two wires shall be 
opposite and about a quarter of an inch asunder, chemi- 
cal action will immediately take place, and gas will con- 
tinue to rise from the extremities of both wires till the 
water has vanished. If an electric spark j^e then sent 
through the tube, the water will reappear. By arrang- 
ing the experiment so as to have the gas^iven out by 
each wire separately, it is found that water consists of 
two volumes of hydrogen and one of oxygen. The hy- 
drogen is given out at the positive wire of the battery, 
and the oxygen at the negative. The oxides are also 
decomposed ; the oxygen appears at the positive pole, 
and the metal at the negative. The decomposition of 
the alkalies and earths by Sir Humphry Davy formed 
a remarkable era in the history of Science. Soda, 
potass, lime, magnesia, and other substances heretofore 



SCT. XXIX. FORMATION OF CRYSTALS. 297 

considered to be simple bodies incapable of decomposi- 
tion, were resolved by electric agency into their constit- 
uent parts, and proved to be metallic oxides, by that 
illustrious philosopher. / All chemical changes produced 
by the electric fluid arfcs accomplished on the same prin- 
ciple ; and it appears that in general, combustible sub- 
stances, metals, and alkalies go to the negative wire, 
while acids and oxygen are evolved at the positive. 
The transfer of these substances to the poles is not the 
least wonderful effect of the Voltaic battery. Though 
the poles be at a considerable distance from one another, 
nay, even in separate vessels, if a communication be 
only established by a quantity of wet thread, as the de- 
composition proceeds the component parts pass through 
the thread in an invisible state, and arrange themselves 
at their respective poles. According to Dr. Faraday, 
electro-chemical decomposition is simply a case of the 
preponderance of one set of chemical affinities more 
powerful in their nature over another set which are less 
powerful. The great efficacy of Voltaic electricity in 
chemical decomposition arises from the continuance of 
its action ; and its agency appears to be most exerted 
on fluids and substances which, by conveying the elec- 
tricity partially and imperfectly, impede its progress. 
But it is now proved to be as efficacious in the compo- 
sition as in the decomposition or analysis of bodies. 

It had been observed that when metallic solutions are 
subjected to galvanic action, a deposition of metal, some- 
times in the form of minute crystals, takes place on the 
negative wire. By extending this principle, and em- 
ploying a very feeble Voltaic action, M. Becquerel has 
succeeded in forming crystals of a great proportion of 
the mineral substances, precisely similar to those pro- 
duced by nature. The electric state of metallic veins 
makes it possible that many natural crystals may have 
taken their form from the action -of electricity bringing 
their ultimate particles, when in solution, within the 
narrow sphere of molecular attraction already mentioned 
as the great agent in the formation of solids. Both light 
and motion favor crystalization. Crystals which form 
in different liquids are generally more abundant on the 
side of the iar exposed to the light : and it is well known 



298 ELCETROGILDING. SECT. XXIX. 

that still water, cooled below 32, starts into crystals of 
ice the instant it is agitated. Light and motion are 
intimately connected with electricity, which may there- 
fore have some influence on the laws of aggregation; 
this is the more likely, as a feeble action is alone neces- 
\ sary, provided it be continued for a sufficient time. 
Crystals formed rapidly are generally imperfect and 
soft, and M. Becquerel found that even years of constant 
Voltaic action were necessary for the crystalization of 
some of the hard substances. If this law be general, 
how many ages may be required for the formation of a 
diamond ? 

The deposition of metal from a metallic solution by 
galvanic electricity has been most successfully applied 
to the art of plating and gilding, as well as to the more 
delicate process of copying medals and copper plates. 
Indeed, not metals only, but any object of art or nature 
may be coated with precipitated metal, provided it be 
first covered with the thinnest film of plumbago, which 
renders a non-conductor sufficiently conducting to re- 
ceive the metal. 

Common electricity, on account of its high tension, 
passes through water and other liquids, as soon as it is 
formed, whatever the length of its course may be. Vol- 
taic electricity, on the contrary, is weakened by the dis- 
tance it has to traverse. Pure water is a very bad con- 
ductor ; but ice absolutely stops a current of Voltaic 
electricity altogether, whatever be the power of the bat- 
tery, although common electricity has sufficient power 
to overcome its resistance. Dr. Faraday has discovered 
that this property is not peculiar to water ; that, with a 
few exceptions, bodies which do not conduct electricity 
when solid, acquire that property, and are immediately 
decomposed, when they become fluid ; and in general, 
that decomposition takes place as soon as the solution 
acquires the capacity of conduction, which has led him 
to suspect that the power of conduction may be only a 
consequence of decomposition. 

Heat increases the conducting power of some sub- 
stances for Voltaic electricity, and of the gases for both 
kinds. Dr. Faraday has given a new proof of the con- 
nection between heat and electricity, by showing that 



Sscrr. XXIX. ELECTRICAL FISH. 299 

in general, when a solid which is not a metal becomes 
fluid, it almost entirely loses its power of conducting 
heat, while it acquires a capacity for conducting elec- 
tricity in a high degree. 

The galvanic fluid affects all the senses. Nothing can 
be more disagreeable than the shock, which may even 
be fatal if the battery be very powerful. A bright flash 
of light is perceived with the eyes shut, when one of 
the wires touches the face and the other the hand. By 
touching the ear with one wire and holding the other, 
strange noises are heard, and an acid taste is perceived 
when the positive wire is applied to the tip of the tongue 
and the negative wire touches some other part of it. 
By reversing the poles the taste becomes alkaline. It 
renders the pale light of the glow-worm more intense. 
Dead animals are roused by it, as if they started again 
into life, and it may ultimately prove to be the cause of 
muscular action in the living. 

Several fish possess the faculty of producing electrical 
effects. The most remarkable are the gymnotus elec- 
tricus, found in South America ; and the torpedo, a 
species of ray, frequent in the Mediterranean. The 
electrical action of the torpedo depends upon an appa- 
ratus apparently analogous to the Voltaic pile, which the 
animal has the power of charging at will, consisting of 
membranous columns filled throughout with laminae, sep- 
arated from one another by a fluid. The absolute quan- 
tity of electricity brought into circulation by the torpedo 
is so great, that it affects the decomposition of water, 
has power sufficient to make magnets^ gives very severe 
shocks and the electric spark. It is identical in kind 
with that of the galvanic battery, the electricity of the 
under surface of the fish being the same with the neg- 
ative pole, and that in the upper surface the same with 
the positive pole. Its manner of action is, however, 
somewhat different ; for although the evolution of the 
electricity is continued for a sensible time, it is inter- 
rupted, being communicated by a succession of dis- 
charges. 



300 TERRESTRIAL MAGNETISM. SECT. XXX. 



SECTION XXX. 

Terrestrial Magnetism Magnetic Poles Lines of equal and no Variation 
The Dip The Magnetic Equator Magnetic Intensity Secular, peri- 
odic, and transitory Variations in the Magnetic Phenomena Origin of 
the Mariner's Compass Natural Magnets Artificial Magnets Polarity 
Induction Intensity Hypothesis of two Magnetic Fluids Distribu- 
tion of the Magnetic Fluid Analogy between Magnetism and Electricity. 

IN order to explain the other methods of exciting 
electricity, and the recent discoveries in that science, it 
is necessary to be acquainted with the general theory 
of magnetism, and also with the magnetism of the earth, 
the director of the mariner's compass his guide through 
the ocean. 

The distribution of terrestrial magnetism is very com- 
plicated, and the observations simultaneously made at 
the various magnetic establishments recently formed in 
both hemispheres have changed many of the opinions 
formerly received with regard to that science. 

Its influence, arising from unknown causes in the in- 
terior of the earth, extends over every part of its surface, 
but seems to be independent of the form and of the 
peculiarities of the exterior of our planet (a). Its 
action on the magnetic needle determines the magnetic 
poles of the earth, which do not coincide with the poles 
of rotation. 

Mr. Hansteen of Copenhagen computed, from obser- 
vations in various parts of the world, that there are two 
magnetic poles in each hemisphere, while M. Gauss 
has concluded there is only one in each (A). The 
position of one of these poles was determined by our 
gallant countrymen when endeavoring to accomplish the 
north-west passage round America. It is situate in 70 
5' 17" north latitude, and 96 46' 45" west longitude. 
Another northern magnetic pole is known by observa- 
tion to be in Siberia, somewhat to the north of 60 north 
latitude and in 102 east longitude, so that the two poles 
are 198 46' 45" asunder. In his recent voyage to the 
Antarctic regions Sir James Ross ascertained that one 
of the southern magnetic poles is in 70 south latitude. 



SECT. XXX. THE DIP. 301 

and about 162 east longitude. The position of the 
other south magnetic pole, if it exists, is unknown. 

In consequence of the attraction and repulsion of 
these poles, a needle suspended so as to move freely in 
a horizontal direction, whether it be magnetic or not, 
only remains in equilibrio when in the magnetic meridian, 
that is, when it is .in a place which passes through a 
north and a south magnetic pole. In some places the 
magnetic meridian coincides with the terrestrial me- 
ridian, and m these a magnetic needle freely suspended, 
as in T;he mariner's 'compass, points to the true north ; 
but if it be carried successively to different places on 
the earth's surface its direction will deviate, sometimes 
to the east, and sometimes to the west of the true north. 
Imaginary lines drawn on the globe through all the 
places where the needle points due north and south are 
called lines of no variation. Imaginary lines drawn 
through all those places whore the needle deviates from 
the geographical meridian by an equal quantity, are lines 
of equal variation. 

A magnetic needle suspended so as to be movable 
only in a vertical plane dips, or becomes more and more 
inclined to the horizon the nearer it is brought to a 
magnetic pole, and there it becomes vertical. Lines 
of equal dip are such as may be imagined to pass 
through all those points on the globe where the dipping 
needle makes the same angle with the horizon. In 
some places the dipping needle becomes horizontal, and 
there the influences of the north and south poles are 
balanced, and an imaginary line passing through all such 
places is the magnetic equator. In going north from 
the magnetic equator one end of the dipping needle dips 
more and more till it becomes perpendicular at the 
north magnetic pole, while in proceeding south from 
the magnetic equator the other end of the dipping 
needle dips, and at last becomes perpendicular at the 
south magnetic pole. The magnetic equator does not 
coincide with the terrestrial equator : it appears to be 
an irregular curve passing round the earth, inclined 
to the earth's equator at an angle of about 12, and 
crossing it in several points, the position of which seems 
stiU to be uncertain. According to some accounts, three 
Cc 



302 INTENSITY OF MAGNETIC FORCE. SECT. XXX. 

points have been ascertained in which that curve cuts 
the equator; yet Captain Duperry, who crossed it re- 
peatedly, affirms, from his own observations combined 
with those of M. Jules de Bosville and of Colonel 
Sabine, that it crosses the terrestrial equator in two 
points only, and those diametrically opposite one to the 
other, and not far from the meridian of Paris. One of 
these nodes he places in the Atlantic, the other in the 
Pacific ocean. He finds that the magnetic equator 
deviates but little from the terrestrial equator in that 
part of the Pacific where there are only a few scattered 
islands (6), that as the islands become more frequent 
the deviation increases, and arrives at a maximum both 
to the north and south in traversing the African and 
American continents ; and that the symmetry of the 
northern and southern segments of this curve is much 
greater than was imagined. 

The intensity of the magnetic force is different in dif- 
ferent parts of the earth. If a magnetic needle, freely 
suspended so as to move horizontally, and at rest in a 
magnetic meridian, be drawn any number of degrees 
from that position, it will make a certain number of os- 
cillations before it resumes its state of rest. The inten- 
sity of the magnetic force is determined from these os- 
cillations, in the same manner that the intensity of the 
gravitating and electrical forces is known from the vibra- 
tions of the pendulum and the balance of torsion (c) : 
and in all these cases it is proportional to the squares of 
the number of oscillations performed in a given time, 
consequently a comparison of the number of vibrations 
accomplished by the same needle during the same time 
in different parts of the earth's surface will determine 
the variations in the magnetic action. By this method 
it was discovered that the intensity of the magnetic force 
increases from the equator toward the poles ; but the 
foci of the greatest total intensity of the magnetic force 
seem neither to coincide with the magnetic nor rotatory 
poles of the earth (d). One of these foci, according to 
Colonel Sabine's magnetic chart, is situate about the 47 
south latitude and 140 east longitude, while another of 
less energy is in 60 south latitude and 235 east longi- 
tude. The point of least total magnetic intensity on the 



SICT. XXX. DISTURBANCES. 303 

whole globe is by the same chart about the 25 south 
latitude and 12 west longitude. In the northern hem- 
isphere the foci of maximum intensity are in lat. 54 32' 
N., long. 261 27' E., and lat. 71 20' N., long. 119 57' E., 
according to M. Gauss's calculations. The magnetic 
intensity appears to be doubled in the ascent from the 
equator to Baffin's bay. 

Such are the principal phenomena of terrestrial mag- 
netism, but it is subject to secular, periodical, and tran- 
sient disturbances still imperfectly known. In the north- 
ern hemisphere, the poles, the lines of equal and no 
variation, the equator, and in short the whole system is 
gradually moving toward the east, so that the relations 
observed in Europe two centuries ago have now reached 
the limits between Europe and Asia, while other parts 
of the system have moved gradually over to us from the 
west. In the southern hemisphere the secular motion 
of the poles and of the whole system is in a contrary 
direction. The cause of these secular disturbances is 
altogether unknown. 

The horizontal needle or compass at any one place is 
also subject to periodic and transient perturbations. 
Great disturbances occur on the same day, or nearly on 
the same day, in different years, from causes unknown. 

There are also disturbances which, according to the 
observations of M. Kreil, in Milan, depend on the decli- 
nation of the moon and her distance from the earth ; 
others of shorter duration seem to be intimately con- 
nected with the motion of the sun in regard to the mag- 
netic meridian of the place of observation. In conse- 
quence of the latter, the needle in the same place is 
subject to diurnal variations: in our latitudes the end 
that points to the north moves slowly westward during 
the forenoon, and returns to its mean position about ten 
hi the evening; it then deviates to the eastward and 
again returns to its mean position about ten in the 
morning. 

M. Kupffer of Casan ascertained that there is a noctur- 
nal as well as a diurnal variation, depending in his opinion 
upon a variation in the magnetic equator. Magnetic 
storms, or sudden and great but transient disturbances, 
take place occasionally in the compass, which are per- 



304 CHANGES OF MAGNETIC INTENSITY. SECT. XXX. 

ceived simultaneously over widely extended regions; 
while others of less magnitude and duration occur more 
frequently, and are, equally witty the greater, not amena- 
ble to any known laws. 

The dip is subject to a secular variation, and according 
to Colonel Sabine has been decreasing in northern lati- 
tudes for the last fifty years at the rate of three minutes 
annually, and is probably owing to the secular motion of 
the magnetic equator. There are disturbances also in 
the dip of a periodic nature, and others very transient, 
which M. Kreil attributes to weak shocks of earth- 
quakes, having observed that the greatest vertical dis- 
turbances have almost always coincided with consider- 
able earthquakes even when they occurred in remote 
regions. 

The magnetic intensity is subject to various changes. 
M. Hansteen has found that it has been decreasing an- 
nually at Christiana, London, and Paris at the rate of 
its 235th, 725th, and 1020th parts respectively, which 
he attributes to the motion of the Siberian magnetic 
pole. The moon increases the onagnetic intensity in 
our hemisphere : but her influence differs with her dif- 
ference of position in the heavens. The times of vibra- 
tion of the needle are less when the moon has south 
declination than when she has north, and they are less 
when she is in perigee than in apogee. It is still doubtful 
whether magnetic intensity varies with the height above 
the earth or not. 

The diurnal variation in the horizontal intensity ob- 
served by M. Hansteen at Christiana is probably owing 
to the sun's influence : indeed the whole of the magnetic 
disturbances have been ascribed to that cause ; and he 
has even found a general resemblance between the iso- 
thermal lines and the lines of equal dip on the surface 
of the earth : yet in the present state of our knowledge 
the magnetic phenomena can only be regarded as the 
effects of a combination of causes whose separate action 
is still unknown. 

The inventor of the mariner's compass, like most of 
the early benefactors of mankind, is unknown. It is 
even doubted which nation first made use of magnetic 
polarity to determine positions on the surface of the globe. 



SKCT. XXX. THE MARINER'S COMPASS. 305 

But it is said that a rude form of the compass was in- 
vented in Upper Asia, and conveyed thence by the 
Tartars to China, where the Jesuit missionaries found 
traces of this instrument having been employed as a 
guide to land travelers in very remote antiquity. From 
that the compass spread over the East, and was imported 
into Europe by the Crusaders, and its construction im- 
proved by an artist of Amalfi, on the coast of Calabria. 
It seems that the Chinese only employed twenty-four 
cardinal divisions, which the Germans increased to 
thirty-two, and gave the points the names which they 
still bear. 

The variation of the compass was 'unknown until Co- 
lumbus, during his first voyage, observed that the needle 
declined from t^ie meridian as he advanced across the 
Atlantic. The dip of the. magnetic needle was first no- 
ticed by Robert Norman, in the year 1576. 

Very delicate experiments have shown that all bodies 
are more or less susceptible of magnetism. Many of 
the gems give signs of it ; cobalt and nickel always pos- 
sess the properties of attraction and repulsion. But the 
magnetic agency is most powerfully developed in iron, 
and in that particular ore of iron called the loadstone, 
which consists of the protoxide and the peroxide of iron, 
together with small portions of silica and alumina. A 
metal is often susceptible of magnetism if it only contains 
the 130,000th part of its weight of iron, a quantity too 
small to be detected by any chemical test. 

The bodies in question are naturally magnetic, but 
that property may be imparted by a variety of methods, 
as by friction with magnetic bodies, or juxtaposition to 
them ; but none is more simple than percussion. A bar 
of hard steel, held in the direction of the dip, will be- 
come a magnet on receiving a few smart blows with a 
hammer on its upper extremity ; and M. Hansteen has 
ascertained that every substance has magnetic poles 
when held in that position, whatever the materials may 
be of which it is composed. 

One of the most distinguishing marks of magnetism is 

polarity, or the property a magnet possesses, when freely 

suspended, of spontaneously pointing nearly north and 

south, and always returning to that position wiien dis- 

20 c c 2 



306 POLARITY AND INDUCTION. SECT. XXX. 

turbed. Another property of a magnet is the attraction 
of uninagnetized iron. Both poles of a magnet attract 
iron, which in return attracts either pole of the magnet 
with an equal and contrary force. The magnetic in- 
tensity is most powerful at the poles, as may easily be 
seen by dipping the magnet into iron filings, which will 
adhere abundantly to each pole, while scarcely any 
attach themselves to the intermediate parts. The 
action of the magnet on unmagnetized iron is confined 
to attraction, whereas the reciprocal agency of magnets 
is characterized by a repulsive as well as an attractive 
force, for a north pole repels.a north pole, and a south 
repels a south pole. But a north and a south pole 
mutually attract one another, which proves that there 
are two distinct kinds of magnetic forces, directly op- 
posite in their effects, though similar in their mode of 
action. 

Induction is the power which a magnet possesses of 
exciting temporary or permanent magnetism in such 
bodies in its vicinity as are capable of receiving it. By 
this property the mere approach of a magnet renders 
iron or steel magnetic, the more powerfully the less the 
distance. When the north pole of a magnet is brought 
near to, and in the line with, an unmagnetized iron bar, 
the bar acquires all the properties of a perfect magnet; 
the end next the north pole of the magnet becomes a 
south pole, while the remote end becomes a north pole. 
Exactly the reverse takes place when the south pole is 
presented to the bar ; so that each pole of a magnet 
induces the opposite polarity in the adjacent end of the 
bar, and the same polarity in the remote extremity ; 
consequently the nearest extremity of the bar is at- 
tracted, and the farther repelled ; but as the action is 
greater on the adjacent than on the distant part, the 
resulting force is that of attraction. By induction, the 
iron bar not only acquires polarity, but the power of 
inducing magnetism in a third body ; and although all 
these properties vanish from the iron as soon as the 
magnet is removed, a lasting increase of intensity is 
generally imparted to the magnet itself by the reaction 
of the temporary magnetism of the iron. -Iron acquires 
magnetism more rapidly than steel, yet it loses it us 



Scr. XXX. EDUCTION OF MAGNETISM. 307 

quickly on the removal of the magnet, whereas the 
steel is impressed with a lasting polarity. 

A certain time is requisite for the induction of mag- 
netism, and it may be accelerated by anything that 
excites a vibratory motion in the particles of the steel, 
such as the smart stroke of the hammer, or heat suc- 
ceeded by sudden cold. A steel bar may be converted 
into a magnet by the transmission of an electric discharge 
through it; and as its efficacy is the same in whatever 
direction the electricity passes, the magnetism arises 
from its mechanical operation exciting a vibration among 
the particles of steel. It has been observed that the 
particles of iron easily resume their neutral state after 
induction, but that those of steel resist the restoration 
of magnetic equilibrium, or a return to the neutral state ; 
it is therefore evident, that any cause which removes 
or diminishes the resistance of the particles will tend to 
destroy the magnetism of the steel ; consequently, the 
same mechanical means which develop magnetism will 
also destroy it. On that account a steel bar may lose 
its magnetism by any mechanical concussion, such as by 
falling on a hard substance, a blow with a hammer, and 
heating to redness, which reduces the steel to a state of 
softness. The circumstances which determine whether 
it shall gain or lose, are its position with respect to the 
magnetic equator, and the higher or lower intensity of 
its previous magnetic state. 

Polarity of one kind only cannot exist in any portion 
of iron or steel ; in whatever manner the intensities of 
the two kinds of polarity may be diffused through a mag- 
net, they exactly balance or compensate one another. 
The northern polarity is confined to one-half of a mag- 
net, and the southern to the other, and they are gener- 
ally concentrated in or near the extremities of the bar. 
When a magnet is broken across its middle, each frag- 
ment is at once converted into a perfect magnet ; the 
part which originally had a north pole acquires a south 
pole at the fractured end ; the part that originally had a 
south pole gets a north pole ; and as far as mechanical 
division can be carried, it is found that each fragment, 
however small, is a perfect magnet. 

A comparison of the number of vibrations accomplished 



308 LAW OF MAGNETIC INTENSITY. SECT. XXX. 

by the same needle, during the same time, at different 
distances from a magnet, gives the law of magnetic in- 
tensity, which follows the inverse ratio of the squares of 
the distances, a law that is not affected by the inter- 
vention of any substance whatever between the magnet 
and the needle, provided that substance be not itself 
susceptible of magnetism. Induction and the reciprocal 
action of magnets are therefore subject to the laws of 
mechanics ; but the composition and resolution of the 
forces are complicated, in consequence of four forces 
being constantly in activity, two in each magnet. 

Mr. Were Fox, who has paid much attention to this 
branch of the science, has lately discovered that the law 
of the magnetic force changes from the inverse squares 
of the distances, to the simple inverse ratio, when the 
distance between two magnets is as small as from the 
fourth to the eighth of an inch, or even as much as half 
an inch when the magnets are large. He found, that 
in the case of repulsion, the change takes place at a still 
greater distance, especially when the two magnets differ 
materially in intensity. 

There can hardly be a doubt but that all the phenom- 
ena of magnetism, like those of electricity, may be ex- 
plained on the hypothesis of one ethereal fluid, which is 
condensed or redundant in the positive pole, and deficient 
in the negative ; a theory that accords best with the sim- 
plicity and general nature of the laws of creation ; never- 
theless, Baron Poisson has adopted the hypothesis of 
two extremely rare fluids pervading all the particles of 
iron, and incapable of leaving them. Whether the par- 
ticles of these fluids are coincident with the molecules 
of the iron, or that they only fill the interstices between 
them, is unknown and immaterial. But it is certain that 
the sum of all the magnetic molecules, added to the sum 
of all the spaces between them, whether occupied by 
matter or not, must be equal to the whole volume of the 
magnetic body. When the two fluids in question are 
combined they are inert, so that the substances contain- 
ing them show no signs of magnetism ; but when sepa- 
rate they are active, the molecules of each of the fluids 
attracting those of the opposite kind, and repelling those 
of the same kind. The decomposition of the united 



SECT. XXX. BARON POISSON'S HYPOTHESIS. 309 

fluids is accomplished by the inductive influence of either 
of the separate fluids ; that is to say, a ferruginous body 
acquires polarity by the approach of either the south or 
north pole of the magnet. The magnetic fluids pervade 
each molecule of the mass of bodies, and in all proba- 
bility the electric fluid does the same, though it appears 
to be confined to the surface ; if so, a compensation must 
take place among the internal forces. The electric 
fluid has a perpetual tendency to escape, and does es- 
cape, when not prevented by the coercive power of the 
surrounding air and other non-conducting bodies. Such 
a tendency does not exist in the magnetic fluids, which 
never quit the substance that contains them under any 
circumstances whatever ; nor is any sensible quantity of 
either kind of polarity ever transferred from one part to 
another of the same piece of steel. It appears that the 
two magnetic fluids, when decomposed by the influence 
of magnetizing forces, only undergo a displacement to 
an insensible degree within the body. The action of all 
the particles so displaced upon a particle of the magnetic 
fluid in any particular situation, compose a resultant 
force, the intensity and direction of which it is the prov- 
ince of the analyst to determine. In this manner M. 
Poisson has proved that the result of the action of all 
the magnetic elements of a magnetized body, is a force 
equivalent to the action of a very thin stratum covering 
the whole surface of a body, and consisting of the two 
fluids the austral and the boreal, occupying different 
parts of it ; in other words, the attractions and repul- 
sions externally exerted by a magnet, are exactly the 
same as if they proceeded from a very thin stratum of 
each fluid occupying the surface only, both fluids being 
in equal quantities, and so distributed that their total 
action upon all the points in the interior of the body is 
equal to nothing. Since the resulting force is the differ- 
ence of the two polarities, its intensity must be greatly 
inferior to that of either. 

In addition to the forces already mentioned, there 
must be some coercive force analogous to friction, which 
arrests the particles of both fluids, so as first to oppose 
their separation, and then to prevent their reunion. In 
soft iron the coercive force is either wanting or ex- 



310 ANALOGY OF MAGNETISM SECT. XXX. 

tremely feeble, since the iron is easily rendered mag- 
netic by induction, and as easily loses its magnetism ; 
whereas in steel the coercive force is extremely ener- 
getic, because it prevents the steel from acquiring the 
magnetic properties rapidly, and entirely hinders it 
from losing them when acquired. The feebleness of 
the coercive force in iron, and its energy in steel, with 
regard to the magnetic fluids, is perfectly analogous to 
the facility of transmission afforded to the electric fluid 
by non-electrics, and the resistance it experiences in 
electrics. At every step the analogy between magnet- 
ism and electricity becomes more striking. The agency 
of attraction and repulsion is common to both; the pos- 
itive and negative electricities are similar to the northern 
and southern polarities, and are governed by the same 
laws, namely, that between like powers there is repul- 
sion, and between unlike powers there is attraction. 
Each of these four forces is capable of acting most ener- 
getically when alone ; but as the electric equilibrium is 
restored by the union of the two electric states, and 
magnetic neutrality by the combination of the two polar- 
ities, they respectively neutralize each other when 
joined. All these forces vary inversely as the squares 
of the distances, and consequently come under the same 
mechanical laws. A like analogy extends to magnetic 
and electrical induction. Iron and steel are in a state of 
equilibrium when the two'magnetic polarities conceived 
to reside in them are equally diffused throughout the 
whole mass, so that they are altogether neutral. But 
this equilibrium is immediately disturbed on the approach 
of the pole of a magnet, which by induction transfers 
one kind of polarity to one end of the iron or steel bar, 
and the opposite kind to the other effects exactly simi- 
lar to electrical induction. There is even a correspond- 
ence between the fracture of a magnet and that of an 
electric conductor ; for if an oblong conductor be elec- 
trified by induction, its two extremities will have opposite 
electricities ; and if in that state it be divided across the 
middle, the two portions, when removed to a distance 
from one another, will each retain the electricity that 
has been induced upon it. The analogy, however, does 
not extend to transference. A body may transfer a re- 



SECT. XXX. AND ELECTRICITY. 311 

dundant quantity of positive electricity to another, or 
deprive another of its electricity, the one gaining at the 
expense of the other ; but there is no instance of a body 
possessing only one kind of polarity. With this excep- 
tion, there is such perfect correspondence between the 
theories of magnetic attractions and repulsions and elec- 
tric forces in conducting bodies, that they not only are 
the same in principle, but are determined by the same 
formulae. Experiment concurs with theory in proving 
the identity of these two unseen influences. Hence if 
the electrical phenomena be due to a modification of the 
ethereal medium, the magnetic phenomena must be 
owing to an analogous cause, and therefore, notwithstand- 
ing the high authority of M. Poisson, they must also be 
attributed to the redundancy and defect of only one fluid. 

With reference to the subject of this chapter I have 
received the following information from Colonel Sabine, 
one of the best authorities in this branch of science. 

The passage marked (A) confounds under the com- 
mon term of " magnetic pole," two things which are 
alike distinct in conception and different in reality. 
These are, 1st the localities on the globe where the 
needle is vertical, or the horizontal force ; and 2d 
the localities where the magnetic forces acting on the 
surface of the globe have a maximum intensity, around 
which the isodynamic lines on the surface arrange them- 
selves in curves, and in departing from which in every 
direction (on the surface) the intensity of the force is 
found to decrease. 

The progress of terrestrial magnetism has been greatly 
impeded by mistakes arising from the different under- 
standings which different people have of what is meant 
by the term magnetic pole. It is the more important 
to have clear ideas and a correct knowledge of facts in 
this matter, because the facts of science are not such as 
in any respect to justify a confusion of terms ; not one 
of the localities where the intensity of the force is a 
maximum coincides with a position where the dip is 
90 ; nor does a dip of 90 anywhere coincide with a 
position where the force is a maximum. 

There is in each hemisphere one locality where the 



312 TWO MAGNETIC POLES. SECT. XXX. 

dip is 90, and two localities where the force forms a 
center of greatest intensity around which the isodynamic 
lines arrange themselves. The localities of dip 90 are 
rather spaces than points : they are the major axes of 
small ovals on the surface of the sphere ; consequently 
they are linear rather than circular spaces. The spot 
where Captain Ross observed the needle so nearly ver- 
tical in 1831 marks the approximate position of that lo- 
cality at that epoch. This position is, as Mrs. Som- 
erville states, about 70 north, and 97 west. The 
isodynamic centers in the same hemisphere are situ- 
ated, one in America, the other in Siberia. The ob- 
servations made anterior to 1837, which are collected 
and arranged in Colonel Sabine's report to the British 
Association of that year, gave, when treated by M. 
Gauss according to the formation of the "Allgemeine 
Theorie," the American maximum in 55 north and 97 
west, and the Siberian in 71 north and 116 east. The 
more recent observations of Messrs. Lefroy and I>ocke, 
who have traveled in America expressly for the more 
accurate determination of what appears so important a 
datum in terrestrial physics, and whose results are at 
this moment being arranged on a chart on which Colonel 
Sabine is about to trace the lines of highest intensity in 
America, show that the center of those curves is yet 
farther to the southward by some degrees (consequently 
still more removed from the position where the dip is 
90) than was supposed in 1837. 

The two maxima of force are not of equal strength : 
the Siberian is somewhat the weaker of the two. The 
positions of both undergo secular change, and both in 
the same direction, viz. to the eastward. The secular 
change of the weaker or Siberian maximum is far more 
considerable than that of the other. The secular 
changes of the isoclinal and isogonic curves correspond 
with those of the two systems of forces indicated by 
distinct maxima having unequal movements of transla- 
tion. The higher isoclinal curves are oval, having their 
major axes in the line of direction joining the two points 
of maximum intensity. The general arrangement in the 
south hemisphere is strictly analogous : but the two 
centers of force are at this epoch separated by a less in- 



SICT. XXX. THE MAGNETIC ATLAS. 313 

terval of longitude than in the north hemisphere. Their 
respective longitudes, derived from the observations of 
the antarctic expedition which Colonel Sabine has re- 
duced and published in the Phil. Trans., are approxi- 
mately 130 and 220 east. The latitudes are not de- 
rivable from the observations with equal approximation ; 
but they do not appear to differ much from the corres- 
ponding latitudes in the north ; i. e. the stronger about 
50 or 55 south, and the weaker about 70 south. Here 
also the weaker maximum has a very considerable sec- 
ular movement, amounting, as Colonel Sabine has given 
reason to believe in the Phil. Trans, of last year, to 
nearly 50 of longitude in 250 years : the secular change 
in the southern hemisphere being to the westward, 
while that in the northern is to the eastward. 

The dip of 90 is far removed from either of these 
localities ; its approximate position may be called about 
73 south and 147 east; but the isoclinal curve of 89 
will doubtless be more correctly given when the Pagoda 
returns from the completion of the survey, and when 
the whole of the observations in the southern hemis- 
phere are combined and treated according to the formulae 
of the * Allgemeine Theorie." 

The object of the geographical branch of the magnetic 
observations of the last few years has been to obtain 
determinations, with the improved instruments of the 
present time, in every accessible part of the globe, with 
a view of combining the results into magnetic charts of 
the three elements drawn directly from the observations, 
and corresponding to the present epoch. The Magnetic 
Atlas will then be recomputed by the methods described 
in Gauss' " Allgemeine Theorie." The observation part 
is nearly accomplished. 

(a) This is by no means established ; the distribution 
of land and water appears to have considerable influence 
on the form of the magnetic equator, as Mrs. Somer- 
ville states at (6). 

(c) In the balance of torsion, the intensity of electrical 
forces is not measured by oscillations, but by the torsiojj 
necessary to destroy the deviation produced* 

(d) Refer to note (4). 

Dn 



314 ELECTRO-MAGNETISM. SECT. XXXI. 



SECTION XXXI. 

Discovery of Electro-Magnetism Deflection of the Magnetic Needle by a 
Current of Electricity Direction of the Force Rotatory Motion by Elec- 
tricity Rotation of a Wire and a Magnet Rotation of a Magnet about 
its Axis Of Mercury and Water Electro- Magnetic Cylinder or Helix 
Suspension of a Needle in a Helix Electro-Magnetic Induction Tem- 
porary Magnets The Galvanometer. 

THE disturbing effects of the aurora borealis and light- 
.ning on the mariner's compass had been long known. 
In the year 1819, M. Oersted, Professor of Natural 
Philosophy at Copenhagen, discovered that a current of 
Voltaic electricity exerts a powerful influence on a mag- 
netized needle. This observation has given rise to the 
theory of electro-magnetism the most interesting sci- 
ence of modern times, whether it be considered as lead- 
ing us a step farther in generalization, by identifying 
two agencies hitherto referred to different causes, or as 
developing a new force, unparalleled in the system of 
the world, which, overcoming the retardation from fric- 
tion, and the obstacle of a resisting medium, maintains 
a perpetual motion, often vainly attempted, but appa- 
rently impossible to be accomplished by means of any 
other force or combination of forces than the one in 
question. 

When the two poles of a Voltaic battery are connect- 
ed by a metallic wire, so as to complete a circuit, the 
electricity flows without ceasing. If a straight portion 
of that wire be placed parallel to, and horizontally above, 
a magnetized needle at rest in the magnetic meridian, 
but freely poised like the mariner's compass, the action 
of the electric current flowing through the wire will 
instantly cause the needle to change its position. Its 
extremity will deviate from the north toward the east 
or west, according to the direction in which the current 
is flowing ; and on reversing the direction of the current, 
the motion of the needle will be reversed also. The 
numerous experiments that have been made on the 
magnetic and electric fluids, as well as those on the vari- 
ous relative motions of a magnetic needle under the 
influence of galvanic electricity, arising from all possible 



Scr. XXXf. DEFLECTION OP THE NEEDLE. 315 

positions of the conducting wire, and every direction of 
the Voltaic current, together with all the other phe- 
nomena of electro-magnetism, are explained by Dr. 
Roget in some excellent articles on these subjects in the 
Library of Useful Knowledge. 

All the experiments tend to prove that the force 
emanating from the electric current, which produces 
such effects on the magnetic needle, acts at right angles 
to the current, and is therefore unlike any force hith- 
erto known. The action of all the forces in nature is 
directed in straight lines, as far as we know ; for the 
curves described by the heavenly bodies result from the 
composition of two forces ; whereas that which is ex- 
erted by an electrical current upon either pole of a 
magnetic has no tendency to cause the pole to approach 
or recede, but to rotate about it. If the stream of elec- 
tricity be supposed to pass through the center of a circle 
whose plane is perpendicular to the current, the di- 
rection of the force exerted by the electricity will always 
be in the tangent to the circle, or at right angles to its 
radius (N. 217). Consequently the tangential force of 
the electricity has a tendency to make the pole of a 
magnet move in a circle round the wire of the battery. 
Mr. Barlow has proved that the action of each particle 
of the electric fluid in the wire, on each particle of the 
magnetic fluid in the needle, varies inversely as the 
squares of the distances. 

Rotatory motion was suggested by Dr. Wollaston. 
Dr. Faraday was the first who actually succeeded in 
making the pole of a magnet rotate about a vertical 
conducting wire. In order to limit the action of the 
electricity to one pole, about two-thirds of a small mag- 
net were immersed in mercury, the lower end being 
fastened by a thread to the bottom of the vessel con- 
taining the mercury. When the magnet was thus floating 
almost vertically with its north pole above the surface, a 
current of positive electricity was made to descend per- 
pendicularly through a wire touching the mercury, and 
immediately the magnet began to rotate from left to 
right about the wire. The force being uniform, the 
rotation was accelerated till the tangential force was 
balanced by the resistance of the mercury, when it be- 



316 ROTATION BY ELECTRICITY. SECT. XXXI. 

came constant. Under the same circumstances the 
south pole of the magnet rotates from right to left. It 
is evident from this experiment, that the wire may also 
be made to perform a rotation round the magnet, since 
the action of the current of electricity on the pole of the 
magnet must necessarily be accompanied by a corres- 
ponding reaction of the pole of the magnet on the elec- 
tricity in the wire. This experiment has been accom- 
plished by a vast number of contrivances, and even a 
small battery, consisting of two plates, has performed 
the rotation. Dr. Faraday produced both motions at 
the same time in a vessel containing mercury ; the wire 
and the magnet revolved in one direction about a com- 
mon center of motion, each following the other. 

The next step was to make a magnet, and also a cyl- 
inder, revolve about their own axes, which they do with 
great rapidity. Mercury has been made to rotate by 
means of Voltaic electricity, and Professor Ritchie has 
exhibited in the Royal Institution the singular spectacle 
of the rotation of water by the same means, while the 
vessel containing it remained stationary. The water 
was in a hollow double cylinder of glass, and on being 
made the conductor of electricity, was observed to re- 
volve in a regular vortex, changing its direction as the 
poles of the battery were alternately reversed. Pro- 
fessor Ritchie found that all the diiferent conductors 
hitherto tried by him, such as water, charcoal, &c., give 
the same electro-magnetic results when transmitting the 
same quantity of electricity, and that they deflect the 
magnetic needle in an equal degree, when their res- 
pective axes of conduction are at the same distance from 
it. But one of the most extraordinary effects of the 
new force is exhibited by coiling a copper wire, so as to 
form a helix or corkscrew, and connecting the extremi- 
ties of the wires with the poles of a galvanic battery. 
If a magnetized steel bar or needle be placed within the 
screw, so as to rest upon the lower part, the instant a 
current of electricity is sent through the wire of the 
helix, the steel bar starts up by the influence of this in- 
visible power, and remains suspended in the air in op- 
position to the force of gravitation (N. 218). The effect 
of the electro-magnetic power exerted by each turn of 



XXXI. ELECTRO-MAGNETIC INDUCTION 317 

the wire is to urge the north pole of the magnet in one 
direction, and the south pole in the other. The force 
thus exerted is multiplied in degree and increased in ex- 
tent by each repetition of the turns of the wire, and in 
consequence of these opposing forces the bar remains 
suspended. This helix has all the properties of a mag- 
net while the electrical current is flowing through it, 
and may be substituted for one in almost every experi- 
ment. It acts as if it had a north pole at one extremity 
and a south pole at the other, and is attracted and re- 
pelled by the poles of a magnet exactly as if it were one 
itself. All these results depend upon the course of the 
electricity ; that is, on the direction of the turns of the 
screw, according as it is from right to left, or from left 
to right, being contrary in the two cases. 

The action of Voltaic electricity on a magnet is not 
only precisely the same with the action of two magnets 
on one another, but its influence in producing temporary 
magnetism in iron and steel is also the same with mag- 
netic induction. The term induction, when appb'ed to 
electric currents, expresses the power which these 
currents possess of inducing any particular state upon 
matter in their immediate neighborhood, otherwise neu- 
tral or indifferent. For example, the connecting wire 
of a galvanic battery holds iron filings suspended like an 
artificial magnet, as long as the current continues to 
flow through it ; and the most powerful temporary mag- 
nets that have ever been made are obtained by bending 
a thick cylinder of soft iron into the form of a horse- 
shoe, and surrounding it with a coil of thick copper wire 
covered with silk, to prevent communication between 
its parts. When this wire forms part of a galvanic cir- 
cuit, the iron becomes so highly magnetic, that a tem- 
porary magnet of this kind, made by Professor Henry, 
of the Albany Academy, in the United States, sustained 
nearly a ton weight. The iron loses its magnetic power 
the instant the electricity ceases to circulate, and ac- 
quires it again as instantaneously when the circuit is re- 
newed. Temporary magnets have been made by Pro- 
fessor Moll of Utrecht, upon the same principle, capable 
of supporting 200 pounds' weight, by means of a battery 
of one plate less than half an inch square, consisting of 

DD2 



318 ELECTRO-MAGNETIC INDUCTION. SKCT. XXXI. 

two metals soldered together. It is truly wonderful 
that an agent, evolved by so small an instrument, and 
diffused through a large mass of iron, should communi- 
cate a force which seems so disproportionate. Steel 
needles are rendered permanently magnetic by electrical 
induction ; the effect is produced in a moment, and as 
readily by juxtaposition as by contact ; the nature of 
the poles depends upon the direction of the current, 
and the intensity is proportional to the quantity of elec- 
tricity. 

It appears that the principle and characteristic phe- 
nomena of the electro-magnetic science are, the evolu- 
tion of a tangential and rotatory force exerted between 
a conducting body and a magnet ; and the transverse 
induction of magnetism by the conducting body in such 
.substances as are susceptible of it. 

The action of an electric current causes a deviation of 
the compass from the plane of the magnetic meridian. 
In proportion as the needle recedes from the meridian, 
the intensity of the force of terrestrial magnetism in- 
creases, while at the same time the electro-magnetic 
force diminishes ; the number of degrees at which the 
needle stops, showing where the equilibrium between 
these two forces takes place, will indicate the intensity 
of the galvanic current. The galvanometer, constructed 
upon this principle, is employed to measure the inten- 
sity of galvanic currents collected and conveyed to it by 
wires. This instrument is rendered much more sensi- 
ble by neutralizing the effects of the earth's magnetism 
on the needle, which is accomplished by placing a sec- 
ond magnetized needle so as to counteract the action of 
the earth on the first a precaution requisite in all del- 
icate magnetica} experiments. 

'Electro-magnetic induction has been elegantly and 
usefully employed by Professor Wheatstone as a mov- 
ing power in a telegraph, by which intelligence is con- 
veyed in a time quite inappreciable, since the electricity 
would make the circuit of the globe in the tenth of a 
second. 



Scr. XXXII. ELECTRO-DYNAMICS. 319 



SECTION XXXII. 

Electro- Dynamics Reciprocal Action of Electric Currents Identity of 
Electro-Dynamic Cylinders and Magnets Differences between the Ac- 
tion of Voltaic Electricity and Electricity of Tension Effects of a Voltaic 
Current Ampere's Theory. 

THE science of electro-magnetism, which must ren- 
der the name of M. Oersted ever memorable, relates to 
the reciprocal action of electrical and magnetic currents : 
M. Ampere, by discovering the mutual action of elec- 
trical currents on one another, has added a new branch 
to the subject, to which he has given the name of elec- 
tro-dynamics. 

When electric currents are passing through two con- 
ducting wires, so suspended or supported as to be capa- 
ble of moving both toward ?.nd from one another, they 
show mutual attraction or repulsion, according as the 
currents are flowing in the same or in contrary direc- 
tions ; the phenomena varying with the relative inclina- 
tions and positions of the streams of electricity. The 
mutual action of such currents, whether they flow in the 
same or in contrary directions, whether they be parallel, 
perpendicular, diverging, converging, circular, or heliacal, 
all produce different kinds of motion in a conducting 
wire, both rectilineal and circular, and also the rotation 
of a wire helix, such as that described, now called aii 
electro-dynamic cylinder, on account of some improve- 
ments in its construction (N. 219). And as the hypoth- 
esis of a force varying inversely as the squares of the 
distances accords perfectly with all the observed phe- 
nomena, these motions come under the same laws of 
dynamics and analysis as any other branch of physics. 

Electro-dynamic cylinders act on each other precisely 
as if they were magnets during the time the electricity 
is flowing through them. All the experiments that can 
be performed with the cylinder might be accomplished 
with a magnet. That end of the cylinder in which the 
current of positive electricity is moving hi a direction 
similar to the motion of the hands of a watch, acts as the 
south pole of a magnet, and the other end, in which the 



320 ACTION OF ELECTRIC CURRENTS. SECT. XXXH. 

current is flowing in a contrary direction, exhibits north- 
ern polarity. 

The phenomena mark a very decided difference be- 
tween the action of electricity in motion or at rest, that 
is, between Voltaic and common electricity ; the laws 
they follow are in many respects of an entirely different- 
nature, though the electricities themselves are identical. 
Since Voltaic electricity flows perpetually, it cannot be 
accumulated, and consequently has no tension, or ten- 
dency to escape from the wires which conduct it. Nor 
do these wires either attract or repel light bodies -in 
their vicinity, whereas ordinary electricity can be accu- 
mulated in insulated bodies to a great degree, and in 
that state of rest the tendency to escape is proportional 
to the quantity accumulated and the resistance it meets 
with. In ordinary electricity, the law of action is that 
dissimilar electricities attract, and similar electricities 
repel one another. , In Voltaic electricity, on the con- 
^trary, similar currents, or such as are moving in the 
same direction, attract one another, while a mutual re- 
pulsion is exerted between dissimilar currents, or such 
as flow in opposite directions. Common electricity 
escapes when the pressure of the atmosphere is re- 
moved, but the electro-dynamical effects are the same 
whether the conductors be in air or in vacuo. 

The effects produced by a current of electricity de- 
pend upon the celerity of its motion through a conduct- 
ing wire. Yet we are ignorant whether the motion be 
uniform or varied, but the method of transmission has a 
marked influence on the results ; for when it flows with- 
out intermission, it occasions a deviation in the magnetic 
needle, but it has no effect whatever when its motion is 
discontinuous or interrupted, like the current produced 
by the common electrical machine when a communica- 
tion is made between the positive and negative con- 
ductors. 

M. Ampere has established a theoiy of electro-mag- 
netism suggested by the analogy between electro-dy- 
namic cylinders and magnets, founded upon the recip- 
rocal attraction of electric currents, to which all the phe- 
nomena of magnetism and electro-magnetism may be 
reduced, by assuming that the magnetic properties 



BKCT. XXXII. ACTION OF ELECTRIC CURRENTS. 321 

which bodies possess derive these properties from cur- 
rents of electricity circulating about every part in one 
uniform direction. Although every particle of a magnet 
possesses like properties with the whole, yet the general 
effect is the same as if the magnetic properties were 
confined to the surface. Consequently the internal elec- 
tro-currents must compensate one another, and there- 
fore the magnetism of a body is supposed to arise from 
a superficial current of electricity constantly circulating 
in a direction perpendicular to the axes of the magnet; 
so that the reciprocal action of magnets, and all the phe- 
nomena of electro-magnetism, are reduced to the action 
and reaction of superficial currents of electricity acting 
at right angles to then* direction. Notwithstanding the 
experiments made by M. Ampere to elucidate the sub- 
ject, there is still an uncertainty in the theory of the 
induction of magnetism by an electric current in a body 
near it. It does not appear whether electric currents 
which did not previously exist are actually produced by 
induction, or if its effects be only to- give one uniform 
direction to the infinite number of electric currents pre- \ 
viously existing in the particles of the body, and thus 
rendering them capable of exhibiting magnetic phenom- 
ena, in the same manner as polarization reduces those 
undulations of light to one plane which had previously 
been performed in every plane. Possibly both may be 
combined in producing the effect ; for the action of an 
electric current may not only give a common direction 
to those already existing, but may also increase their 
intensity. However that may be, by assuming that the 
attraction and repulsion of the elementary portions of 
electric currents vary inversely as the squares of the 
distances, the action being at right angles to the direc- 
tion of the current, it is found that the attraction and 
repulsion of a current of indefinite length on the ele- 
mentary portion of a parallel current at any distance 
from it, is in the simple ratio of the shortest distance 
between them. Consequently the reciprocal action of 
electric currents is reduced to the composition and res- 
olution of forces, so that the phenomena of electro-mag- 
netism are brought under the laws of dynamics by the 
theory of M. Ampere. 
21 



322 MAGflETO-ELECTrmCITY. SECT. XXXlli. 



SECTION XXXIII. 

Magneto-Electricity Volta-Electric Induction Magneto-Electric Induc- 
tion Identity in the Action of Electricity and Magnetism Description 
of a Magneto-Electric Apparatus and its Effects Identity of Magnetism 
and Electricity. 

FROM the law of action and reaction being equal and 
contrary, it might be expected that, as electricity pow- 
erfully affects magnets, so, conversely, magnetism ought 
to produce electrical phenomena. By proving this veiy 
important fact from the following series of interesting 
and ingenious experiments, Dr. Faraday has added 
another branch to the science, which he has named 
magneto-electricity. A great quantity of copper wire 
was coiled in the form of a helix round one half of a 
ring of soft iron, and connected with a galvanic battery ; 
while a similar helix connected with a galvanometer was 
wound round the other half of the ring, but not touching 
the first helix. As soon as contact was made with the 
battery, the needle of the galvanometer was deflected. 
But the action was transitory ; for when the contact 
was continued, the needle returned to its usual position, 
and was not affected by the continual flow of the electri- 
city through the wire connected with the battery. As 
soon however as the contact was broken, the needle of 
the galvanometer was again deflected, but in the con- 
trary direction. Similar effects were produced by an 
apparatus consisting of two helices of copper wire coiled 
round a block of wood, instead of iron, from which Dr. 
Faraday infers that the electric current passing from the 
battery through one wire, induces a similar current 
through the other wire, but only at the instant of con- 
tact, and that a momentary current is induced in a con- 
trary direction when .the passage of the electricity is 
suddenly interrupted. These brief currents or waves 
of electricity were found to be capable of magnetizing 
needles, of passing through a small extent of fluid, and 
when charcoal points were interposed in the current of 
the induced helix, a minute spark was perceived as often 



S*cr. XXXlil. VOLTA-ELECTllHJ INDUCTION. 3^3 

as the contacts were made or broken, but neither chem- 
ical action nor any other electric effects were obtained. 
A deviation of the needle of the galvanometer took place 
when common magnets were employed instead of the 
Voltaic current; so that the magnetic and electric 
fluids are identical in their effects in this experiment. 
Again, when a helix formed of 220 feet of copper wire, 
into which a cylinder of soft iron was introduced, was 
placed between the north and south poles of two bar 
magnets, and connected with the galvanometer by means 
of wires from each extremity, as often as the magnets 
were brought into contact with the iron cylinder, it be- 
came magnetic by induction, and produced a deflection 
in the needle of the galvanometer. On continuing the 
contact, the needle resumed its natural position, and 
when the contact was broken, deflection took place in 
the opposite direction ; when the magnetic contacts 
were reversed, the deflection was reversed also. With 
strong magnets, so powerful was the action, that the 
needle of the galvanometer whirled round several times 
successively ; and similar effects were produced by the 
mere approximation or removal of the heb'x to the poles 
of the magnets. Thus it was proved that magnets pro- 
duce the veiy same effects on the galvanometer that 
electricity does. Though at that time no chemical de- 
composition was effected by these momentary currents 
which emanate from the magnets, they agitated the 
limbs of a frog ; and Dr. Faraday justly observes, that 
"an agent which is conducted along metallic wires in 
the manner described, which, while so passing, pos- 
sesses the peculiar magnetic actions and force of a cur- 
rent of electricity, which can agitate and convulse the 
limbs of a frog, and which finally can produce a spark 
by its discharge through charcoal, can only be electri- 
city." Hence it appears that electrical currents are 
evolved by magnets, which produce the same phenomena 
with the electrical currents from the Voltaic battery : 
they however differ materially in this respect that 
time is required for the exercise of the magnetico-elec- 
trie induction, whereas Volta-electric induction is in- 
stantaneous. 

After Dr. Faraday had proved the identity of the 



324 MAGNETO-ELECTRIC APPARATUS. SECT. XXXII. 

magnetic and electric fluids by producing the spark, 
heating metallic wires, and accomplishing chemical 
decompositions, it was easy to increase these effects by 
more powerful magnets and other arrangements. The 
apparatus now in use is in effect a battery where the 
agent is the magnetic instead of the Voltaic fluid, or in 
other words, electricity, and is thus constructed. 

A very powerful horseshoe magnet, formed of twelve 
steel plates in close approximation, is placed in a hori- 
zontal position. An armature, consisting of a bar of the 
purest soft iron, has each of its ends bent at right 
angles, so that the faces of those ends may be brought 
directly opposite and close to the poles of the magnet 
when required. Ten copper wires covered with silk, 
in order to insulate them are wound round one half of 
the bar of soft iron, as a compound helix: ten other 
wires, also insulated, are wound round the other half of 
the bar. The extremities of the first set of wires are in 
metallic connection with a circular disc, which dips into 
a cup of mercury, while the ends of the other ten wires 
in the opposite direction are soldered to a projecting 
screw-piece, which carries a slip of copper with two 
opposite points. The steel magnet is stationary ; but 
when the armature, together with its appendages, is 
made to rotate vertically, the edge of the disc always 
remains immersed in the mercury, while the points of 
the copper slip alternately dip in it and rise above it. 
By the ordinary laws of induction, the armature becomes 
a temporary magnet while its bent ends are opposite 
the poles of the steel magnet, and ceases to be magnetic 
when they are at right angles to them. It imparts its 
temporaiy magnetism to the helices which concentrate 
it ; and while one set conveys a current to the disc, the 
other set conducts the opposite current to the copper slip. 
As the edge of the revolving disc is always immersed in 
the mercury, one set of wires is constantly maintained 
in contact with it, and the circuit is only completed 
when a point of the copper slip dips in the mercury 
also ; but the circuit is broken the moment that point 
rises above it. Thus, by the rotation of the armature, 
the circuit is alternately broken and renewed ; and as 
it is only at these moments that electric action is mani- 



SECT. XXXIV. ELECTRICITY FROM ROTATION. 325 

Tested, a brilliant spark takes place every time the cop- 
per point leaves the surface of the mercury. Platina 
wire is ignited, shocks smarts enough to be disagreeable 
are given, and water is decomposed with astonishing 
rapidity by the same means; which proves beyond a 
doubt the identity of the magnetic and electric agencies, 
and places Dr. Faraday, whose experiments established 
the principle, in the first rank of experimental philoso- 
phers. 



SECTION XXXIV. 

Electricity produced by Rotation Direction of the Currents Electricity 
from the Rotation of a Magnet M. Arago's Experiment explained 
Rotation of a Plate of Iron between the Poles of a Magnet Relation of 
Substances to Magnets of three kinds Thermo- Electricity. 

M. ARAGO discovered an entirely new source of mag- 
netism in rotatory motion. If a circular plate of copper 
be made to revolve immediately above or below a mag- 
netic needle or magnet, suspended in such a manner 
that the magnet may rotate in a plane parallel to that of 
the copper plate, the magnet tends to follow the circum- 
volution of the plate ; or if the magnet revolves, the 
plate tends to follow its motion : so powerful is the 
effect, that magnets and plates of many pounds weight 
have been carried round. This is quite independent of 
the motion of the air, since it is the same when a pane 
of glass is interposed between the magnet and the cop- 
per. When the magnet and the plate are at rest, not 
the smallest effect, attractive, repulsive, or of any kind, 
can be perceived between them. In describing this 
phenomenon, M. Arago states that it takes place not 
only with metals, but with all substances, solids, liquids, 
and even gases, although the intensity depends upon 
the kind of substance in motion. Experiments made 
by Dr. Faraday explain this singular action. A plate 
of copper, twelve inches in diameter and one-fifth of an 
inch thick, was placed between the poles of a powerful 
horseshoe magnet, and connected at certain points with 
a galvanometer by copper wires. When the plate was 
at rest no effect was produced ; but as soon as the plate 
EE 



326 DIRECTION OF THE CURRENTS SECT. XXXIV. 

was made to revolve rapidly, the galvanometer needle 
was deflected sometimes as much as 90, and, by a uni- 
form rotation, the deflection was constantly maintained 
at 45. When the motion of the copper plate was je- 
versed, the needle was deflected in the contrary direc- 
tion, and thus a permanent current of electricity was 
evolved by an ordinary magnet. The intensity of the 
electricity collected by the wires, and conveyed by them 
to the galvanometer, varied with the position of the 
plate relatively to the poles of the magnet. 

The motion of the electricity in the copper plate may 
be conceived by considering, that merely by moving a 
single wire like the spoke of a wheel before a magnetic 
pole, a current of electricity tends to flow through it 
from one end to the other. Hence, if a wheel be con- 
structed of a great many such spokes, and revolved 
near the pole of a magnet in the manner of the copper 
disc, each radius or spoke will tend to have a current 
produced in it as it passes the pole. Now, as the 
circular plate is nothing more than an infinite number 
of radii or spokes in contact, the currents will flow in 
the direction of the radii if a channel be open for their 
return, and in a continuous plate that channel is afforded 
by the lateral portions on each side of the particular 
radius close to the magnetic pole. This hypothesis is 
confirmed by observation, for the currents of positive 
electricity set from the center to the circumference, and 
the negative from the circumference to the center, and 
vice versa, according to the position of the magnetic 
poles and the direction of rotation. So that a collecting 
wire at the center of the copper plate conveys positive 
electricity to the galvanometer in one case, and negative 
in another ; that collected by a conducting wire in con- 
tact with the circumference of the plate is always the 
opposite of the electricity conveyed from the center. 
It is evident that when the plate and magnet are both 
at rest, no effect takes place, since the electric currents 
which cause the deflection of the galvanometer cease 
altogether. The same phenomena may be produced by 
electro-magnets. The effects are similar when the 
magnet rotates and the plate remains at rest. When 
the magnet revolves uniformly, about its own axis, elec- 



SECT. XXXIV. DIRECTION OF THE CURRENTS. 327 

tricity of the same kind is collected at its poles, and the 
opposite electricity at its equator. 

The phenomena which take place in M. Arago's 
experiments may be explained on this principle. When 
both the copper plate and the magnet are revolving, the 
action of the induced electric current tends continually 
to diminish then* relative motion, and to bring the mov- 
ing bodies into a state of relative rest : so that if one be 
made to revolve by an extraneous force, the other will 
tend to revolve about it in the same direction, and with 
the same velocity. 

When a plate of iron, or of any substance capable of 
being made either a temporary or permanent magnet, 
revolves between the poles of a magnet, it is found that 
dissimilar poles on opposite sides of the plate neutralize 
each other's effects, so that no electricity is evolved; 
while similar poles on each side of the revolving plate 
increase the quantity of electricity, and a single pole 
end-on is sufficient. But when copper, and substances 
not sensible to ordinary magnetic impressions, revolve, 
similar poles on opposite sides of the plate neutralize 
each other; dissimilar poles on each side exalt the 
action : and a single pole at the edge of the revolving 
plate, or end-on, does nothing. This forms a test for 
distinguishing the ordinary magnetic force from that 
produced by rotation. If unlike poles, that is, a north 
and south pole, produce more effect than one pole, the 
force will be due to electric currents ; if similar poles 
produce more effect than one, then the power is not 
electric. These investigations show that there are 
really very few bodies magnetic in the manner of iron. 
Dr. Faraday therefore arranges substances in three 
classes, with regard to their relation to magnets : those 
affected by the magnet when at rest, like iron, steel, 
and nickel, which possess ordinary magnetic properties ; 
those affected when in motion, in which electric cur- 
rents are evolved by the inductive force of the magnet, 
such as copper ; and, lastly, those which are perfectly 
indifferent to the magnet, whether at rest or in motion. 

It has already been observed, that three bodies are 
requisite to form a galvanic circuit, one of which must 
be fluid. But in 1822, Professor Seebeck, of Berlin, 



328 THERMO-ELECTRICITY. SECT. XXXIV- 

discovered that electric currents may be produced by 
the partial application of heat to a circuit formed of two 
solid conductors. For example, when a semicircle of 
bismuth, joined to a semicircle of antimony, so as to form 
a ring, is heated at one of the junctions by a lamp, a 
current of electricity flows through the circuit from the 
antimony to the bismuth, and such thermo-electric cur- 
rents produce all the electro-magnetic effects. A com- 
pass needle placed either within or without the circuit, 
and at a small distance from, it, is deflected from its na- 
tural position, in a direction corresponding to the way in 
which the electricity is flowing. If such a ring be sus- 
pended so as to move easily in any direction, it will obey 
the action of a magnet brought near it, and may even 
be made to revolve. According to the researches of M. 
Seebeck, the same substance, unequally heated, exhibits 
electrical currents ; and M. Nobili observed, that in all 
metals, except zinc, iron, and antimony, the electricity 
flows from the hot part toward that which is cold. That 
philosopher attributes terrestrial magnetism to a differ- 
ence in the action of heat on the various substances of 
which the crust of the earth is composed ; and in con- 
firmation of his views he has produced electrical currents 
by the contact of two pieces of moist clay, of which one 
was hotter than the other. 

M. Becquerel constructed a thermo-electric battery of 
one kind of metal, by which he has determined the re- 
lation between the heat employed and the intensity of 
the resulting electricity. He found that in most metals 
the intensity of the current increases with the heat to a 
certain limit, but that this law extends much farther in 
metals that are difficult to fuse, and which do not rust. 
The experiments of Professor Gumming show that the 
mutual action of a magnet and a thermo-electric current 
is subject to the same laws as those of magnets and gal- 
vanic currents, consequently all the phenomena of repul- 
sion, attraction, and rotation maybe exhibited by a thermo- 
electric current. M. Botto, of Turin, has decomposed 
water and some solutions by thermo-electricity ; and 
very recently the Cav. Antinori of Florence has suc- 
ceeded in obtaining a brilliant spark with the aid of an 
electro-dynamic coil. 



SECT. XXXV. TERRESTRIAL MAGNETISM. 329 

The principle of thermo-electricity has been employed 
by MM. Nobili and Melloni for measuring extremely 
minute quantities of heat in their experiments on the 
instantaneous transmission of radiant caloric. The 
thermo-rnultiplier, which they constructed for that pur- 
pose, consists of a series of alternate bars, or rather fine 
wires of bismuth and antimony, placed side by side, and 
the extremities alternately soldered together. When 
heat is applied to one end of this apparatus, the other 
remaining at its natural temperature, currents of elec- 
tricity flow through each pair of bars, which are conveyed 
by wires to a delicate galvanometer, the needle of which 
points out the intensity of the electricity conveyed, and 
consequently that of the heat employed. This instru- 
ment is so delicate that the comparative warmth of dif- 
ferent insects has been ascertained by means of it. 



SECTION XXXV. 

The Action of Terrestrial Magnetism upon Electric Currents Induction 
of Electric Currents by Terrestrial Magnetism The Earth Magnetic by 
Induction Mr. Barlow's Experiment of an Artificial Sphere The Heat 
of the Sun the Probable Cause of Electric Currents in the Crust of the 
Earth ; and of the Variations in Terrestrial Magnetism Electricity of 
Metallic Veins Terrestrial Magnetism possibly owing to Rotation 
Magnetic Properties of the Celestial Bodies Identity of the Five Kinds 
of Electricity Connection between Light, Heat, and Electricity or Mag- 
netism. 

IN all the experiments hitherto described, artificial 
magnets alone were used ; but it is obvious that the 
magnetism of the terrestrial spheroid, which has so 
powerful an influence on the mariner's compass, must 
also affect electrical currents. It consequently appears 
that a piece of copper wire bent into a rectangle, and 
free to revolve on a vertical axis, arranges itself with its 
plane at right angles to the magnetic meridian, as soon 
as a stream of electricity is sent through it. Under the 
same circumstances a similar rectangle, suspended on a 
horizontal axis at right angles to the magnetic meridian, 
assumes the same inclination with the dipping needle ; 
so that terrestrial magnetism has the same influence on 
electrical currents as an artificial magnet. But the 
magnetic action of the earth also induces electric cur- 

E E2 



330 EARTH MAGNETIC BY INDUCTION. SECT. XXXV. 

rents. When a hollow helix of copper wire, whose 
extremities are connected with the galvanometer, is 
placed in the magnetic dip, and suddenly inverted sev- 
eral times, accommodating the motion to the oscillations 
of the needle, the latter is soon made to vibrate through 
an arc of 80 or 90. Hence it is evident, that what- 
ever may be the cause of terrestrial magnetism, it pro- 
duces currents of electricity by its direct inductive power 
upon a metal not capable of exhibiting any of the ordi- 
nary magnetic properties. The action on the galvanom- 
eter is much greater when a cylinder of soft iron is 
inserted into the helix, and the same results follow the 
simple introduction of the iron cylinder into, or removal 
out of, the helix. These effects arise from the iron 
being made a temporary magnet by the inductive action 
of terrestrial magnetism ; for a piece of iron, such as a 
poker, becomes a magnet for the time, when placed in 
the line of the magnetic dip. 

M. Biot has formed a theory of terrestrial magnetism 
upon the observations of M. de Humboldt as data. As- 
suming that the action of two opposite magnetic poles 
of the earth upon any point is inversely as the squares 
of the distances, he obtains a general expression for the 
direction of the magnetic needle, depending upon the 
distance between the north and south magnetic poles ; 
so that if one of these quantities varies, the correspond- 1 
ing variation of the other will be known. By making 
the distance between the poles vary, and comparing the 
resulting direction of the needle with the observations 
of M. de Humboldt, he found that the nearer the poles 
are supposed to approach to one another, the more the 
computed and observed results agree ; and when the 
poles were assumed to coincide, or nearly so, the differ- 
ence between theory and observation is the least possi- 
ble. It is evident, therefore, that the earth does not 
act as if it were a permanently magnetic body, the dis- 
tinguishing characteristic of which is, to have two poles 
at a distance from one another. Mr. Barlow has inves- 
tigated this subject with much skill and success. He 
first proved that the magnetic power of an iron sphere 
resides in its surface ; he then inquired what the super- 
ficial action of an iron sphere in a state of transient mag- 



SECT. XXXV. THE EARTH NOT A REAL MAGNET. 331 

netic induction, on a magnetized needle, would be, if 
insulated from the influence of terrestrial magnetism. 
The results obtained, corroborated by the profound 
analysis of M. Poisson, on the hypothesis of the two 
poles being indefinitely near the center of the sphere, 
are identical with those obtained by M. Biot for the 
earth from M. de Humboldt's observations. Whence 
it follows, that the laws of terrestrial magnetism deduced 
from the formulae of M. Biot, are inconsistent with those 
which belong to a permanent magnet, but that they are 
perfectly concordant with those belonging to a body in a 
state of transient magnetic induction. The earth, there- 
fore, is to be considered as only transiently magnetic by 
induction, and not a real magnet. Mr. Barlow has ren- 
dered this extremely probable by forming a wooden 
globe, with grooves admitting of a copper wire being 
coiled round it parallel to the equator from pole to pole. 
When a current of electricity was sent through the 
wire, a magnetic needle suspended above the globe, and 
neutralized from the influence of the earth's magnetism, 
exhibited all the phenomena of the dipping and varia- 
tion needles, according to its positions with regard to 
the wooden globe. As there can be no doubt that the 
same phenomena would be exhibited by currents of 
thermo, instead of Voltaic electricity, if the grooves of 
the wooden globe were filled by rings constituted of two 
metals, or of one metal unequally heated, it seems highly 
probable that the heat of the sun may be a great agent 
in developing electric currents in or near the surface of 
earth, by its action upon the substances of which the 
globe is composed, and by changes in its intensity, may 
occasion the diurnal variation of the compass, and the 
other vicissitudes in terrestrial magnetism evinced by 
the disturbance in the direction of the magnetic lines, in 
the same manner as it influences the parallelism of the 
isothermal lines. That such currents do exist in metal- 
liferous veins appears from the experiments of Mr. Fox 
in the Cornish mines. Even since the last edition of 
this book was published, Mr. Fox has obtained additional 
proof of the activity of electro-magnetism under the 
earth's surface. He has shown that not only the nature 
of the metalliferous deposits must have been determined 



332 EARTH MAGNETIC BY ROTATION. SECT. XXXV. 

by their relative electrical conditions, but that the direc- 
tion of the metallic veins must have been influenced by 
the direction of the magnetic meridians ; and in fact 
almost all the metallic deposits in the world tend from 
east to west, or from northeast to southwest. Though 
it is impossible to say in the present state of our knowl- 
edge, how far the sun may be concerned in the phe- 
nomena of terrestrial magnetism, it is probable that the 
secular and periodic disturbances in the magnetic force 
are occasioned by a variety of other combining circum- 
stances. Among these M. Biot mentions the vicinity of 
mountain chains to the place of observation, and still 
more the action of extensive volcanic fires, which change 
the chemical state of the terrestrial surface, they them- 
selves varying from age to age, some becoming extinct, 
while others burst into activity. Should the ethereal 
medium which fills space be the same with the electric 
fluid, as M. Mossotti. supposes, may not the heat of the 
sun rarefy it at the earth's equator, and thus by the in- 
equality of its distribution, and its superior density at 
the poles, occasion some of the magnetic phenomena of 
the globe ? and may not the sun's motion in decimation 
cause temporary variations of density in the fluid, and 
produce periodic changes in the magnetic equator and 
intensity ? Were this the case, all the planets would 
be magnets like the earth, being precisely in similar cir- 
cumstances. 

It is moreover probable, that terrestrial magnetism 
may be owing, in a certain extent, to the earth's rota- 
tion. Dr. Faraday has proved that all the phenomena 
of revolving plates may be produced by the inductive 
action of the earth's magnetism alone. If a copper plate 
be connected with a galvanometer by two copper wires, 
one from the center and another from the circumference, 
in order to collect and convey the electricity, it is found 
that when the plate revolves in a plane passing through 
the line of the dip, the galvanometer is not affected. 
But as soon as the plate is inclined to that plane, elec- 
tricity begins to be developed by its rotation ; it becomes 
more powerful as the inclination increases, and arrives 
at a maximum when the plate revolves at right angles to 
the line of the dip. When the revolution is in the samo 



Strr. XXXV. EARTH MAGNETIC BY ROTATION. 333 

direction with that of the hands of a watch, the current 
of electricity flows from its center to the circumference ; 
and when the rotation is in the opposite direction, the 
current sets the contrary way. The greatest deviation 
of the galvanometer amounted to 50 or 60, when the 
direction of the rotation was accommodated to the oscil- 
lations of the needle. Thus a copper plate, revolving in 
a plane at right angles to the line of the dip, forms a new 
electrical mnchine, differing from the common plate- 
glass machine, by the material of which it is composed 
being the most perfect conductor, whereas glass is the 
most perfect non-conductor ; besides, insulation, which 
is essential in the glass machine, is fatal in the copper 
one. The quantity of electricity evolved by the metal 
does not appear to be inferior to that developed by the 
glass, though very different in intensity. 

From the experiments of Dr. Faraday, and^lso from 
theory, it is possible that the rotation of the earth may 
produce electric currents in its own mass. In that case, 
they would flow superficially in the meridians, and if 
collectors could be applied at the equator, and poles, as 
in the revolving plate, negative electricity would be col- 
lected at the equator, and positive at the poles ; that is 
to say, there would be a deficiency at the equator and a 
redundancy at the poles ; but without something equiv- 
alent to conductors to complete the circuit, these cur- 
rents could not exist. 

Since the motion, not only of metals but even of fluids, 
when under the influence of powerful magnets, evolves 
electricity, it is probable that the gulf-stream may exert 
a sensible influence upon the forms of the lines of mag- 
netic variation, in consequence of electric currents mov- 
ing across it, by the electro-magnetic induction of the 
earth. Even a ship, passing over the surface of the 
water in northern or southern latitudes, ought to have 
electric currents running directly across the line of her 
motion. Dr. Faraday observes, that such is the facility 
with which electricity is evolved by the earth's magnet- 
ism, that scarce any piece of metal can be moved in 
contact with others without a development of it, and 
consequently, among the arrangements of steam-engines 
and metallic machinery, curious electro-magnetic coin- 



334 MAGNETISM OF SUN AND PLANETS. SECT. XXXV. 

binations probably exist, which have never yet been no- 
ticed. 

According to the observations of MM. Biot and Gay- 
Lussac, during their aerostatic expedition, the magnetic 
action is not confined to the surface of the earth, but 
extends into space. The moon has become highly 
magnetic by induction, in consequence of her proximity 
to the earth, and because her greatest diameter always 
points toward it. Her influence on terrestrial magnetism 
is now ascertained : the magnetism of the hemisphere 
that is turned toward the earth attracts the pole of our 
needles that is turned toward the south, and increases 
the magnetism of our hemisphere ; and as the magnetic, 
like the gravitating force, extends through space, the 
induction of the sun, moon, and planets must occasion 
perpetual variations in the intensity of terrestrial mag- 
netism, by the continual changes in their relative posi- 
tions. 

Jn the brief sketch that has been given of the five 
kinds of electricity, those points of resemblance have 
been pointed out which are characteristic of one indi- 
vidual power. But as many anomalies have been lately 
removed, and the identity of the different kinds placed 
beyond a doubt by Dr. Faraday, it may be satisfactory 
to take a summary view of the various coincidences in 
their modes of action on which their identity has been so 
ably and completely established by that great electrician. 

The points of comparison are attraction and repulsion 
at sensible distances, discharge from points through air, 
the heating power, magnetic influence, chemical decom- 
position, action on the human frame, and lastly, the spark. 

Ordinary electricity is readily discharged from points 
through air, but Dr. Faraday found that no sensible ef- 
fect takes place from a Voltaic battery consisting of 140 
double plates, either through air or in the exhausted 
receiver of an air-pump, the tests of the discharge being 
the electrometer and chemical action, a circumstance 
owing to the small degree of tension, for an enormous 
quantity of electricity is required to make these effects 
sensible, and for that reason they cannot be expected 
from the other kinds, which are much inferior in de- 
gree. Common electricity passes easily through rare- 



SstT. XXXV. IDENTITY OF THE ELECTRICITIES. 335 

fied and hot air, and also through flame. Dr. Faraday 
effected chemical decomposition and a deflection of the 
galvanometer by the transmission of Voltaic electricity 
through heated air, and observes that these experiments 
are only cases of the discharge which takes place through 
air between the charcoal terminations of the poles of a 
powerful battery when they are gradually separated 
after contact for the air is then heated. Sir Humphry 
Davy mentions that, with the original Voltaic apparatus 
at the Royal Institution, the discharge passed through 
four inches of air ; that, in the exhausted receiver of an 
air-pump, the electricity would strike through nearly 
half an inch of space, and the combined effects of rare- 
faction and heat upon the included air were such as to 
enable it to conduct the electricity through a space of six 
or seven inches. A Leyden jar may be ^instantaneously 
charged with Voltaic, and also with magneto-electricity 
another proof of their tension. Such effects cannot be 
obtained frojn the other kinds, on account of their weak- 
ness only. 

The heating powers of ordinary and Voltaic electri- 
city have long been known, but the world is indebted to 
Dr. Faraday for the wonderful discovery of the heating 
power of the magnetic fluid : there is no indication of 
heat either from the animal or thermo electricities. All 
kinds of electricity have strong magnetic powers, those 
of the Voltaic fluid are highly exalted, and the existence 
of the magneto and thermo electricities was discovered 
by their magnetic influence alone. The needle has 
been deflected by all in the same manner, and magnets 
have been made by all according to the same laws. 
Ordinary electricity was long supposed incapable of de- 
flecting the needle ; M. Colladon and Dr. Faraday how- 
ever have proved that, in this respect also, ordinary elec- 
tricity agrees with Voltaic, but that time must be allowed 
for its action. It deflected the needle, whether the cur- 
rent was sent through rarefied ah-, water, or wire. 
Numerous chemical decompositions have been effected 
by ordinary and Voltaic electricity, according to the 
same laws and modes of arrangement. Dr. Davy de- 
composed water by the ejfictricity of the torpedo, Dr. 
Faraday accomplished its decompositToii, ancTTJrTRitchie 



336 IDENTITY OF THE ELECTRICITIES. SECT. XXXV. 

its composition, by means of magnetic, action ; and M. 
Botto of Turin has shownHhe chemical effects of the 
thftfirua-pJer'.t-.rrcjty in the decomposition of water, and 
some other substances. The* elecjj^e and ggkMwic 
shock, the flash in the eyes, and~thesensation on the 
tongue, are well known. All these effects are produced 
by magneto-electricity, even to a painful degree. The 
torpetfcTand gyifmOTTTT^lectricus give severe shocks, and 
the limbs of a frog have been convulsed by thermo-elec- 
tricity. The last point of comparison is the spark, 
which is common to the ordinary Voltaic and magnetic 
fluids ; and Professor Linari, of Siena, has very lately 
obtained both the direct and induced sparks from the 
torpedo, proving that in this respect aniraal_eltricity 
does not differ from the others. Indeed, the conclusion 
drawn by Dr. Faraday is that the five kinds of electri- 
city are identical, and that the differences of intensity 
and quantity are quite sufficient to account for what 
were supposed to be their distinctive qualities. He has 
given still greater assurance of their identity by showing 
that the magnetic force and the chemical action of elec- 
tricity are in direct proportion to the absolute quantity 
of the fluid which passes through the galvanometer, 
whatever its intensity may be. 

In light, heat, and electricity, or magnetism, nature 
has exhibited principles which do not occasion any ap- 
preciable change in the weight of bodies, although their 
presence is manifested by the most remarkable mechan- 
ical and chemical action. These agencies are so con- 
nected, that there is reason to believe they will ulti- 
mately be referred to some one power of a higher order, 
in conformity with the general economy of the system 
of the world, where the most varied and complicated 
effects are produced by a small number of universal 
laws. These principles penetrate matter in all direc- 
tions ; their velocity is prodigious, and their intensity 
varies inversely as the squares of the distances. The 
development of electric currents, as well by magnetic 
as electric induction, the similarity in their mode of ac- 
tion in a great variety of circumstances, but above all, 
the production of the spark from a magnet, the ignition 
of metallic wires, and chemical decomposition, show that 



SKCT. XXXVI. COMETS. 337 

magnetism can no longer be regarded as a separate in- 
dependent principle. Although the evolution of light 
and heat during the passage of the electric fluid may be 
from the compression of the air, yet the development 
of electricity by heat, the influence of heat on magnetic 
bodies, and that of light on the vibration of the compass, 
show an occult connection between all these agents, 
which probably will one day be revealed. In the mean 
time it opens a noble field of experimental research to 
philosophers of the present, perhaps of future ages. 



SECTION XXXVI. 

Ethereal Medium Comets Do not disturb the Solar System Their 
Orbits and Disturbances M. Faye's Comet, probably the same with 
Level's Periods of other three known Halley's Acceleration in the 
Mean Motions of Encke's and Biela's Comets The Shock of a Comet- 
Disturbing Action of the Earth and Planets on Encke's and Biela's 
Comets Velocity of Comets The Great Comet of 1843 Physical Con- 
stitution Shine by borrowed Light Estimation of their Number. 

IN considering the constitution of the earth and the 
fluids which surround it, various subjects have presented 
themselves to our notice, of which some, for aught we 
know, are confined to the planet we inhabit ; some are 
common to it and to the other bodies of our system. 
But an all-pervading ether probably fills the whole visi- 
ble creation, and conveys, in the form of light, tremors 
which may have been excited in the deepest recesses 
of the universe thousands of years before we were called 
into being. The existence of such a medium, though 
at first hypothetical, is nearly proved by the undulatory 
theory of light, and rendered all but certain within a 
few years by the motion of comets, and by its action 
upon the vapors of which they are chiefly composed. 
It has often been imagined, that, in addition to the ef- 
fects of heat and electricity, the tails of comets have 
infused new substances into our atmosphere. Possibly 
the earth may attract some of that nebulous matter, 
since the vapors raised by the sun's heat, when the 
comets are in perihelio, and which form their tails, are 
scattered through space in their passage to their aphe- 
lion ; but it has hitherto produced no effect, nor have 
22 FF 



338 EARTH NOT AFFECTED BY COMETS. SECT.XXXVI. 

the seasons ever been influenced by these bodies. The 
light of the comet of the year 1811, which was so bril- 
liant, did not impart any heat even when condensed on 
the bulb of a thermometer, of a structure so delicate 
that it would have made the hundredth part of a degree 
evident. In all probability, the tails of comets may have 
passed over the earth without its inhabitants being con- 
scious of their presence ; and there is reason to believe 
that the tail of the great comet of J1843 did so. 

The passage of comets has never sensibly disturbed 
the stability of the solar system ; their nucleus, being in 
general only a mass of vapor, is so rare, and their transit 
so rapid, that the time has not been long enough to ad- 
mit of a sufficient accumulation of impetus to produce a 
perceptible action. Indeed M. Dusejour has proved, 
that under the most favorable circumstances, a comet 
cannot remain longer than two hours and a half at a less 
distance from the earth than 10,500 leagues. The 
comet of 1770 passed within about six times the distance 
of the moon from the earth, without even affecting our 
tides. According to La Place, the action of the earth 
on the comet of 1770 augmented the period of its revolu- 
tion by more than two days ; and if comets had any per- 
ceptible disturbing energy, the reaction of the comet 
ought to have increased the length of our year. Had 
the mass of that comet been equal to the mass of the 
earth, its disturbing action would have increased the 
length of the sidereal year by 2 1 ' 53 ; but as Delainbre's 
computations from the Greenwich observations of the 
sun show that the length of the year has not been in- 
creased by the fraction of a second, its mass could not 
have been equal to the ^ l (T ^th part of that of the earth. 
This accounts for the same comet having twice swept 
through the system of Jupiter's satellites without de- 
ranging the motion of these moons. M. Dusejour has 
computed that a comet, equal in mass to the earth, pass- 
ing at the distance of 12,150 leagues from our planet, 
would increase the length of the year to 367 lt 16 h 5' n , and 
the obliquity of the ecliptic as much as 2. So the 
principal action of comets would be to alter the calendar, 
even if they were dense enough to affect the earth. 

Comets traverse all parts of the heavens ; their paths 



SCT. XXXVI. ORBITS OF COMETS. 339 

have every possible inclination to the plane of the eclip- 
tic, and, unlike the planets, the motion of more than 
half of those that have appeared has been retrograde, 
that is, from east to west. They are only visible when 
near their perihelia; then their velocity is such, that its 
square is twice as great as that of a body moving in a 
circle at the same distance : they consequently remain 
but a very short time within the planetary orbits. And 
as all the conic sections of the same focal distance sen- 
sibly coincide, through a small arc, on each side of the 
extremity of their axis, it is difficult to ascertain in which 
of these curves the comets move, from observations 
made, as they necessarily must be, at their perihelia 
(N. 220). Probably they all move in extremely eccen- 
tric ellipses; although in most cases the parabolic curve 
coincides most nearly with their observed motions. 
Some few seem to describe hyperbolas; such, being once 
visible to us, would vanish forever, to wander through 
boundless space, to the remote systems of the universe. 
If a planet be supposed to revolve in a circular orbit, the 
radius of which is equal to the perihelion distance of a 
comet moving in a parabola, the areas described by these 
two bodies in the same time will be as unity to the 
square root of two, which forms such a connection be- 
tween the motion of comets and planets, that by Kep- 
ler's law, the ratio of the areas described during the 
same time by the comet and the earth may be found. 
So that the place of a comet may be computed at any 
time in its parabolic orbit, estimated from the instant of 
its passage at the perihelion. It is a problem of very 
great difficulty to determine all the other elements of 
parabolic motion namely, the comet's perihelion dis- 
tance, or shortest distance from the sun, estimated in 
parts of the mean distance of the earth from the sun; 
the longitude of the perihelion ; the inclination of the 
orbit on the plane of the ecliptic ; and the longitude of 
the ascending node. Three observed longitudes and 
latitudes of a comet are sufficient for computing the ap- 
proximate values of these quantities; but an accurate 
estimation of them can only be obtained by successive 
corrections, from a number of observations, distant from 
one another. When the motion of a comet is retrograde, 



340 PARABOLIC ELEMENTS. SECT. XXXVI. 

tho place of the ascending node is exactly opposite to 
what it is when the motion is direct. Hence the place 
of the ascending node, together with the direction of the 
comet's motion, show whether the inclination of the 
orbit is on the north or south side of the plane of the 
ecliptic. If the motion be direct, the inclination is on 
the north side ; if retrograde, it is on the south side. 

The identity of the elements is the only proof of the 
return of a comet to our system. Should the elements 
of a new comet be the same, or nearly the same, with 
those of any one previously known, the probability of 
the identity of the two bodies is very great, since the 
similarity extends to no less than four elements, every 
one of which is capable of an infinity of variations. But 
even if the orbit be determined with all the accuracy the 
case admits of, it may be difficult, or even impossible, 
to recognize a comet on its return, because its orbit 
would be very much changed if it passed near any of 
the large planets of this or of any other system, in con- 
sequence of their disturbing energy, which would be 
very great on bodies of so rare a nature. 

By far the most curious and interesting instance of 
the disturbing action of the great bodies of our system 
is found in the comet of 1770. The elements of its or- 
bit, determined by Messier, did not agree with those of 
any comet that had hitherto been computed, yet Lexel 
ascertained that it described an ellipse about the sun, 
whose major axis was. only equal to three times the 
length of the diameter of the terrestrial orbit, and con- 
sequently that it must return to the sun at intervals of 
five years and a half. This result was confirmed by 
numerous observations, as the comet was visible through 
an arc of 170 ; yet this comet had never been observed 
before the year 1770, nor has it ever again been seen 
till 1843, though very brilliant. The disturbing action 
of the larger planets affords a solution of this anomaly, 
as Lexel ascertained that in 1767 the comet must have 
passed Jupiter at a distance less than the fifty-eighth 
part of its distance from the sun, and that in 1779 it 
would be 500 times nearer Jupiter than the sun ; conse- 
quently the action of the sun on the comet would not be 
the fiftieth part of what it would experience from Jupi- 



SECT. XXXVI. LEXEL'S COMET. 341 

ter, so that Jupiter became the primum mobile. As- 
suming the orbit to be such as Lexel had determined in 
1770, La Place found that the action of Jupiter, previ- 
ous to the year 1770, had so completely changed the 
form of it, that the comet which had been invisible to us 
before 1770, was then brought into view, and that the 
action of the same planet producing a contrary effect, 
has subsequently to that year removed it from our sight, 
since it was computed to be revolving in an orbit whose 
perihelion was beyond the orbit of Ceres. However, 
the action of Jupiter during the summer of 1840 must 
have been so great, from his proximity to that singular 
body, that he seems to have brought it back to its former 
path, as he had done in 1767, for the elements of the 
orbit of a comet which was discovered in November, 
1843, by M. Faye, agree so nearly with those of the 
orbit of Lexel's comet as to leave scarcely a doubt of 
their identity. From the smallness of the eccentricity, 
the orbit resembles those of the planets, but this comet 
is liable to greater perturbations than any other body in 
the system, because it comes very near the orbit of 
Mars when in perihelion, and very near that of Jupiter 
when in aphelion ; besides, it passes within a compara- 
tively small distance of the orbits of the minor planets, 
and as it will continue to cross the orbit of Jupiter at 
each revolution till the two bodies meet, its periodic 
time, now about seven years, will again be changed, but 
in the mean time it ought to return to its perihelion in 
the year 1851. This comet might have been seen from 
the earth in 1776, had its light not been eclipsed by that 
of the sun. It is quite possible that comets frequenting 
our system may be turned away, or others brought to 
the sun, by the attraction of planets revolving beyond 
the orbit of Uranus, or by bodies still farther removed 
from the solar influence. 

Other three comets, liable to less disturbance, return 
to the sun at stated intervals. Halley computed the 
elements of the orbit of a comet that appeared in the 
year 1682, which agreed so nearly with those of the 
comets of 1607 and 1531, that he concluded it to be the 
same body returning to the sun at intervals of about 
seventy-five years. He consequently predicted its re- 
FF2 



342 HALLEY'S COMET. SECT. XXXVI. 

appearance in the year 1758, or in the beginning of 
1759. Science was not sufficiently advanced in the time 
of Halley^ to enable him to determine the perturbations 
this comet might experience ; but Clairaut computed, 
that in consequence of the attraction of Jupiter and 
Saturn, its periodic time would be so much shorter than 
during its revolution between 1607 and 1682, that it 
would pass its perihelion on the 18th of April, 1759. 
The comet did arrive at that point of its orbit on the 12th 
of March, which was thirty-seven days before the time 
assigned. Clairaut subsequently reduced the error to 
twenty-three days ; and La Place has since shown that 
it would only have been thirteen days if the mass of 
Saturn had been as well known as it is now. It appears 
from this, that the path of the comet was not quite known 
at that period ; and although many observations were 
then made, they were far from attaining the accuracy of 
those of the present day. Besides, since the year 1759 
the orbit of the comet has been altered by the attraction 
of Jupiter in one direction, and that of the earth, Saturn, 
and Uranus, in the other; yet, notwithstanding these 
sources of uncertainty, and our ignorance of all the pos- 
sible causes of derangement from unknown bodies on 
the confines of our system, or in the regions beyond it, 
the comet has appeared exactly at the time, and not far 
from the place, assigned to it by astronomers ; and its 
actual arrival at its perihelion a little before noon on the 
16th of November, 1835, only differed from the com- 
puted time by a veiy few days. 

The fulfilment of this astronomical prediction is truly 
wonderful if it be considered that the comet is seen only 
for a few weeks, during its passage through our system, 
and that it wanders from the sun for seventy-five years 
to twice the distance of Uranus. This enormous orbit 
is four times longer than it is broad ; its length is about 
3420 millions of miles, or about thirty-six times the mean 
distance of the earth from the sun. At its perihelion 
the comet comes within nearly fifty-seven millions of 
miles of the sun, and at its aphelion it is sixty times 
more distant. On account of this extensive range it 
must experience 3600 times more light and heat, when 
nearest to the sun than in the most remote point of its 



Scr. XXXVI. HALLEY'S COMET. 343 

orbit. In the one position the sun will seem to be four 
times larger than he appears to us, and at the other he 
will not be apparently larger than a star (N. 221). 

On the first appearance of Halley's comet, early in 
August, 1835, it seemed to be merely a globular mass of 
dim vapor, without a tail. A concentration of light, a 
little on one side of the center, increased as the comet 
approached the sun and earth, and latterly looked so 
like the disc of a small planet, that it might have been 
mistaken for a solid nucleus. M. Struve, however, saw 
a central occultation of a star of the ninth magnitude by 
the comet, at Dorpat, on the 29th of September. The 
star remained constantly visible, without any considera- 
ble diminution of light ; and instead of being eclipsed, 
the nucleus of the comet disappeared at the moment of 
conjunction from the brilliancy of the star. The tail 
increased as the comet approached its perihelion, and 
shortly before it was lost in the sun's rays, it was between 
thirty and forty degrees in length. 

According to the observations of M. Valz, of Nismes, 
the nebulosity increased in magnitude as it approached 
the sun ; but no other comet on record has exhibited 
such sudden and unaccountable changes of aspect. The 
nucleus, clear and well defined, like the disc of a planet, 
was observed on one occasion to become obscure and en- 
larged hi the course of a few hours. But by far the 
most remarkable circumstance was the sudden appear- 
ance of certain luminous brushes or sectors, diverging 
from the center of the nucleus through the nebulosity. 
M. Struve describes the nucleus of the comet, in the 
beginning of October, as elliptical, and like a burning 
coal, out of which there issued, in a direction nearly op- 
posite to the tail, a divergent flame, varying in intensity, 
form, and direction, appearing occasionally even double, 
and suggesting the idea of luminous gas bursting from 
the nucleus. On one occasion M. Arago saw three of 
these divergent flames on the side opposite the tail, rising 
through the nebulosity, which they greatly exceeded in 
brilliancy : after the comet had passed its perihelion, it 
acquired another of these luminous fans, which was ob- 
served by Sir John Herschel at the Cape of Good Hope. 
Hevelius describes an appearance precisely similar. 



344 HALLEY'S COMET. SECT. XXXVI. 

which he had witnessed in this comet at its approach to 
the sun in the year 1682, and something of the kind 
seems to have been noticed in the comet of 1744. Pos- 
sibly the second tail of the comet of 1724, which was 
directed toward the sun, may have been of this nature. 

The influence of the ethereal medium on the motions 
of Halley's comet, will be known after another revolu- 
tion, and future astronomers will learn, by the accuracy 
of its returns, whether it has met with any unknown 
cause of disturbance in its distant journey. Undiscovered 
planets, beyond the visible boundary of our system, may 
change its path and the period of its revolution, and thus 
may indirectly reveal to us their existence, and even 
their physical nature and orbit. The secrets of the yet 
more distant heavens may be disclosed to future genera- 
tions by comets which penetrate still farther into space, 
such as that of 1763, which, if any faith may be placed 
in the computation, goes nearly forty-three times farther 
from the sun than Halley's does, and shows that the 
sun's attraction is powerful enough, at the enormous 
distance of 15,500 millions of miles, to recall the comet 
to its perihelion. The periods of some comets are said 
to be of many thousand years, and even the average time 
of the revolution of comets generally is about a thousand 
years ; which proves that the sun's gravitating force ex- 
tends very far. La Place estimates that the solar at- 
traction is felt throughout a sphere whose radius is a 
hundred millions of times greater than the distance of 
the earth from the sun. 

Authentic records of Halley's comet do not extend be- 
yond the year 1456, yet it may be traced, with some 
degree of probability, even to a period preceding the 
Christian em. But as the evidence only rests upon 
coincidences of its periodic time, which may vary as 
much as eighteen months from the disturbing action of 
the planets, its identity with comets of such remote 
times must be regarded as extremely doubtful. 

This is the first comet whose periodicity has been 
established. It is also the first whose elements have 
been determined from observations made in Europe ; for 
although the comets which appeared in the years 240, 
539, 565, and 837, are the most ancient of those whose 



SECT. XXXVI. ENCKE'S COMET. 345 

orbits have been traced, their elements were computed 
from Chinese observations. 

Besides Halley's and Lexel's comets, two others are 
now proved to form part of our system ; that is to say, 
they return to the sun at intervals, one of three years, 
and the other of 6J years nearly. The first, generally 
called Encke's comet, or the comet of the short period, 
was first seen by MM. Messier and Mechain, in 1786, 
again by Miss Herschel hi 1805, and its returns, in the 
years 1805 and 1819, were observed by other astrono- 
mers, under the impression that all four were different 
bodies. However, Professor Encke not only proved 
their identity, but determined the circumstances of the 
comet's motion. Its reappearance in the years 1825, 
1828, and 1832, accorded with the orbit assigned by M. 
Encke, who thus established the length of its period to 
be 1204 days, nearly. This comet is very small, of 
feeble light, and invisible to the naked eye, except 
under very favorable circumstances, and in particular 
positions. It has no tail, it revolves in an ellipse of 
great eccentricity inclined at an angle of 13 22' to the 
plane of the ecliptic, and is subject to considerable per- 
turbations from the attraction of the planets, which 
occasion variations in its periodic time. Among the 
many perturbations to which the planets are liable, 
their mean motions, and therefore the major axes of 
their orbits, experience no change ; while on the con- 
trary, the mean motion of the moon is accelerated from 
age to age a circumstance at first attributed to the re- 
sistance of an ethereal medium pervading space, but 
subsequently proved to arise from the secular diminution 
of the eccentricity of the terrestrial orbit. Although 
the resistance of such a medium has not hitherto been 
perceived in the motions of such dense bodies as the 
planets and satellites, its effects on the revolutions of 
the two small periodic comets hardly leave a doubt of 
its existence. From the numerous observations that 
have been made on each return of the comet of the 
short period, the elements have been computed with 
great accuracy on the hypothesis of its moving in vacua. 
Its perturbations occasioned by the disturbing action of 
the planets have been determined ; and after everything 



346 ENCKE'S COMET. SECT. XXXVL 

that could influence its motion had been duly considered, 
M. Encke found that an acceleration of about two days 
in each revolution has taken place in its mean motion, 
precisely similar to that which would be occasioned by 
the resistance of an ethereal medium. And as it cannot 
be attributed to a cause like that which produces the 
acceleration of the moon, it must be concluded that the 
celestial bodies do not perform their evolutions in an 
absolute void, and that although the medium be too rare 
to have a sensible effect on the masses of the planets 
and satellites, it nevertheless has a considerable influ- 
ence on so rare a body as a comet. Contradictory as it 
may seem, that the motion of a body should be accele- 
rated by the resistance of an ethereal medium, the 
truth becomes evident if it be considered that both 
planets and comets are retained in their orbits by two 
forces which exactly balance one another ; namely, the 
centrifugal force producing the velocity in the tangent, 
and the attraction of the gravitating force directed to 
the center of the sun. If one of these forces be dimin- 
ished by any cause, the other will be proportionally 
increased. Now, the necessaiy effect of a resisting 
medium is to diminish the tangential velocity, so that 
the balance is destroyed, gravity preponderates, the 
body descends toward the sun till equilibrium is again 
restored between the two forces; and as it then de- 
scribes a smaller orbit it moves with increased velocity. 
Thus, the resistance of an ethereal medium actually 
accelerates the motion of a body ; but as the resisting 
force is confined to the plane of the orbit, it has no in- 
fluence whatever on the inclination of the orbit, or on 
the place of the nodes. In computing its effect, M. 
Encke assumed the increase to be inversely as the 
squares of the distances, and that its resistance acts as a 
tangential force proportional to the squares of the 
comet's actual velocity in each point of its orbit. The 
other comet belonging to our system, which returns to 
its perihelion after a period of 6| years, has been ac- 
celerated in its motion by a whole day during its last 
revolution, which puts the existence of ether nearly 
beyond a doubt, and forms a strong presumption in cor- 
roboration of the undulatory theory of light. Since this 



SECT. XXXVI. BIELA*S OR GAMBARTS COMET. 347 

comet, which revolves nearly between the orbits of fhe 
earth and Jupiter, is only accelerated one day at each 
revolution, while Encke's, revolving nearly between the 
orbits of Mercury and Pallas, is accelerated two, the 
ethereal medium must increase in density toward the 
sun. The comet in question was discovered by M. 
Biela at Johannisberg on the 27th of February, 1826, 
and ten days afterward it was seen by M. Gambart at 
Marseilles, who computed its parabolic elements, and 
found that they agreed with those of the comets which 
had appeared in the years 1789 and 1795, whence he 
concluded them to be the same body moving in an 
ellipse, and accomplishing its revolution in 2460 days. 
The perturbations of this comet were computed by M. 
Damoiseau, who predicted that it would cross the plane 
of the ecliptic on the 29th of October, 1832, a little 
before midnight, at a point nearly 18,484 miles within 
the earth's orbit; and as M. Olbers of Bremen, in 1805, 
had determined the radius of the comet's head to be 
about 21,136 miles, it was evident that its nebulosity 
would envelop a portion of the earth's orbit, a circum- 
stance which caused some alarm in France, from the 
notion that if any disturbing cause had delayed the 
arrival of the comet for one month, the earth must have 
passed through its head. M. Arago dispelled these 
fears by his excellent treatise on comets in the An- 
nuaire of 1832, where he proves, that as the earth 
would never be nearer the comet than 18,000,000 
British leagues, there could be no danger of collision. 
The earth is in more danger from these two small 
comets than from any other. Encke's crosses the ter- 
restrial orbit sixty times in a century, and may ulti- 
mately come into collision: but both are so extremely 
rare, that little injury is to be apprehended. 

The earth would fall to the sun in 64i days, if it 
were struck by a comet with sufficient impetus to de- 
stroy its centrifugal force. What the earth's primitive 
velocity may have been, it is impossible to say. There- 
fore a comet may have given it a shock without changing 
the axis of rotation, but only destroying part of its tan- 
gential velocity, so as to diminish the size of the orbit a 
thing by no means impossible, though highly improbable. 



348 THE SHOCK OP A COMET. SECT. XXXVI. 

At all events, there is no proof of this having occurred; 
and it is manifest that the axis of the earth's rotation 
has not been changed, because, as the ether offers no 
sensible resistance to so dense a body as the earth, the 
libration would to this day be evident in the variation it 
must have occasioned in the terrestrial latitudes. Sup- 
posing the nucleus of a comet to have a diameter only 
equal to the fourth part of that of the earth, and that its 
perihelion is nearer to the sun than we are ourselves, its 
orbit being otherwise unknown, M. Arago has computed 
that the probability of the earth receiving a shock from 
it is only one in 281 millions, and that the chance of our 
coming in contact with its nebulosity is about ten or 
twelve times greater. Only comets with retrogade mo- 
tions can come into direct collision with the earth, and if 
the momentum were great the event might be fatal; 
but in general the substance of comets is so rare, that it 
is likely they would not do much harm if they were to 
impinge ; and even then the mischief would probably be 
local, and the equilibrium soon restored, provided the 
nucleus were gaseous, or very small. It is, however, 
more probable that the earth would only be deflected a 
little from its course by the approach of a comet, with- 
out being touched by it. The comets that have come 
nearest to the earth were that of the year 837, which 
remained four days within less than 1,240,000 leagues 
from our orbit; that of 1770, which approached within 
about six times the distance of the moon. The cele- 
brated comet of 1680 also came very near to us ; and 
the comet whose period is 61 years was ten times nearer 
the earth in 1805 than in 1832, when it caused so much 
alarm. 

Encke's and Biela's comets are at present far removed 
from the influence of Jupiter, but they will not always 
remain so, because the aphelia and nodes of the orbits 
of these two comets being the points which approach 
nearest to the orbit of Jupiter, at each meeting of the 
planet and comets which shall take place there, the 
major axi-s of Encke's comet will be increased, and that 
of Biela's diminished, till in the course of time, when 
the proximity has increased sufficiently, the orbits will 
be completely changed, as that of Lexel's was in 1770, 



SKCT. XXXVI. ENCKE'S AND BIELA'S COMETS. 349 

Every twenty-third year, or after seven revolutions of 
Encke's cornet, its greatest proximity to Jupiter takes 
place, and at that lime his attraction increases the pe- 
riod of its revolution by nine days a circumstance 
which took place in the end of the years 1820 and 1843. 
But from the position of the bodies there is a diminution 
of three days in the six following revolutions, which 
reduces the increase to six days in seven revolutions. 
Thus before the year 1819, the periodic time of Encke's 
comei; was 1204 days, and it was 1219 days in accom- 
plishing its last revolution, which terminated in 1845. 
By this progressive increase the orbit of the comet will 
reach that of Jupiter in seven or eight centuries, and 
then by the very near approach of the two bodies it wiH 
be completely changed. 

At present the earth and Mercury have the most 
powerful influence on the motions of Encke's and Biela's 
comets ; and have had for so long a time that, according 
to the computation of Mr. Airy, the present orbit of the 
latter was formed by the attraction of the earth, and 
that of Encke's by the action of Mercury. With re- 
gard to the latter comet, that event must have taken 
place in February, 1776. Tn 1786 Encke's comet had 
both a tail and a nucleus, now it has neither ; a singular 
instance of the possibility of their disappearance. 

Comets in or near their perihelion move with pro- 
digious velocity. That of 1680 appears to have gone 
half round the sun in ten hours and a half, moving at 
the rate of 880,000 miles an hour. If its enormous 
centrifugal force had ceased when passing its perihe- 
lion, it would have fallen to the sun in about three 
minutes, as it was then less than 147,000 miles from his 
surface. So near the sun, it would be exposed to a heat 
27,500 times greater than that received by the earth ; 
and as the sun's heat is supposed to be in proportion to 
the intensity of his light, it is probable that a degree of 
heat so intense would be sufficient to convert into vapor 
every terrestrial substance with which we are acquainted. 
At the perihelion distance the sun's diameter would be 
seen from the comet under an angle of 73, so that the 
sun, viewed from the comet, would nearly cover the 
whole extent of the heavens from the horizon to tho 
GG 



350 FALL OF COMETS TO THE SUN. SECT. XXXVI. 

zenith. As this comet is presumed to have a period of 
575 years, the major axis of its orbit must be so great, 
that at the aphelion the sun's diameter would only sub- 
tend an angle of about fourteen seconds, which is not 
so great by half as the diameter of Mars appears to us 
when in opposition. The sun would consequently im- 
part no heat, so that the comet would then be exposed 
to the temperature of the ethereal regions, which is 58 
below the zero point of Fahrenheit. A body of such 
tenuity as the comet, moving with such velocity, must 
have met with great resistance from the dense atmos- 
phere of the sun, while passing so near his surface at 
its perihelion. The centrifugal force must consequently 
have been diminished, and the sun's attraction propor- 
tionally augmented, so that it must have come nearer to 
the sun in 1680 than in its preceding revolution, and 
would subsequently describe a smaller orbit. As this 
diminution of its orbit will be repeated at each revolu- 
tion, the comet will infallibly end by falling on the sur- 
face of the sun, unless its course be changed by the dis- 
turbing influence of some large body in the unknown 
expanse of creation. Our ignorance of the actual den- 
sity of the sun's atmosphere, of the density of the 
comet, and of the period of its revolution, renders it 
impossible to form any idea of the number of centuries 
which must elapse before this event takes place. 

The same cause may affect the motions of the planets, 
and ultimately be the means of destroying the solar sys- 
tem. But, as Sir John Herschel observes, they could 
hardly all revolve in the same direction round the sun 
for so many ages without impressing a corresponding 
motion on the ethereal fluid, which may preserve them 
from the accumulated effects of its resistance. Should 
this material fluid revolve about the sun like a vortex, it 
will accelerate the revolutions of such comets as have 
direct motions, and retard those that have retrograde 
motions. 

The comet which appeared unexpectedly in the be- 
ginning of the year ]843, was on-e of the most splendid 
that ever visited the solar system. It was in the con- 
stellation of Antinous in the end of January, at a dis- 
tance of 115 millions of miles from the earth, and it 



SCT. XXXVI. COMET OF 1843. 351 

passed through its perihelion on the 27th of February, 
when it was lost in the sun's rays ; but it began to be 
visible about the 3d of March, at which time it was near 
the star Iota Cetae, and its tail extended toward the 
Hare. The brightness of the comet and the length of 
its tail continued to increase till the latter stretched far 
beyond the constellation of the Hare toward a point 
above Sirius. Stars were distinctly seen through it, 
and when near perihelion the comet was so bright that 
it was seen in clear sunshine in the United States 
like a white cloud. The motion was retrograde, and 
on leaving the solar system it retreated so rapidly at 
once from the sun and earth that it was soon lost sight 
of for want of light. On the 1st of April it was between 
the sun and the earth, and only 40 millions of miles from 
the latter ; and as its tail was at least 60 millions of 
miles long, and 20 millions of miles broad, we probably 
passed through it without being aware of it. There is 
some discrepancy in the different computations of the 
elements of the orbit, but in the greater number of 
cases the perihelion distance was found to be less than 
the semidiameter of the sun, so that the comet must 
have grazed his surface, if it did not actually impinge 
obliquely on him. 

The perihelion distance of this comet differs little 
from that of the great comet of 1668, which came so 
near the sun. The motion of both was retrograde, and 
a certain resemblance in the two orbits makes it proba- 
ble that they are the same body performing a revolution 
in 175 years. 

Though already so well acquainted with the motions 
of comets, we know nothing of then* physical constitu- 
tion. A vast number, especially of telescopic comets, 
are only like clouds or masses of vapor, often without 
tails. Such were the comets which appeared in the 
years 1795, 1797, and 1798. But the head commonly 
consists of a concentrated mass of light, like a planet, 
surrounded by a very transparent atmosphere, and the 
whole, viewed with a telescope, is so diaphanous, that 
the smallest star may be seen even through the densest 
part of the nucleus ; in general their solid parts, if they 
have any, are so minute, that they have no sensible 



352 MASSES OF COMETS. SECT. XXXVI. 

diameter, like that of the comet of 1811, which ap- 
peared to Sir William Herschel like a luminous point 
in the middle of the nebulous matter. The nuclei, 
which seemed to be formed of the denser strata of that 
nebulous matter in successive coatings, are sometimes 
of great magnitude. Those comets which came to the 
sun in the years 1799 and 1807, had nuclei whose di- 
ameters measured 180 and 275 leagues respectively, 
and the second comet of 1811 had a nucleus of 1350 
leagues in diameter. 

It must however be stated, that as comets are gene- 
rally at prodigious distances from the earth, the solid 
parts of the nuclei appear like mere points of light, so 
minute that it impossible to measure them with any 
kind of accuracy, so that the best astronomers often 
differ in the estimation of their size, by one-half of the 
whole diameter. The transit of a comet across the sun 
would afford the best information with regard to the 
nature of the nuclei. It was computed that such an 
event was to take place in the year 1827 ; unfortunately 
the sun was hid by clouds from the British astronomers, 
but it was examined at Viviers and at Marseilles at the 
time the comet must have been projected on its disc, 
but no spot or cloud was to be seen, so that it must 
have had no solid part whatever. The nuclei of many 
comets which seemed solid and brilliant to the naked 
eye have been resolved into mere vapor by telescopes 
of high powers ; in Halley's comet there was no solid 
part at all. 

The nebulosity immediately round the nucleus is so 
diaphanous that it gives little light ; but at a small dis- 
tance the nebulous matter becomes suddenly brilliant, 
so as to look like a bright ring round the body. 
Sometimes there are two or three of these luminous 
concentric rings separated by dark intervals, but they 
are generally incomplete on the part next the tail. 

These annular appearances are an optical effect, 
arising from a succession of envelops of the nebulous 
matter with intervals between them, of which the first 
is sometimes in contact with the nucleus and sometimes 
not. The thickness of these bright diaphanous coatings 
in the comets of 1799 and 1807 were about 7000 and 



SECT. XXXVI. ENVELOPS OF COMETS. 353 

10,000 leagues respectively ; and in the first comet of 
1611, the luminous ring was 8000 leagues thick, and 
the distance between its interior surface and the center 
of the head was 10,000 leagues. The latter comet was 
by much the most brilliant that has been seen in mod- 
ern times ; it was first discovered in this country by Mr. 
James Vietch of Inchbonny, and was observed in all its 
changes by Sir William Herschel and M. Olbers. To 
the naked eye, the head had the appearance of an ill- 
defined round mass of light, which was resolved hi to 
several distinct parts when viewed with a telescope. 
A very brilliant interior circular mass of nebulous mat- 
ter was surrounded by a black space having a parabolic 
form, veiy distinct from the dark blue of the sky. This 
dark space was of a very appreciable breadth. Exterior 
to the black interval there was a luminous parabolic 
contour of considerable thickness, which was prolonged 
on each side in two diverging branches, which formed 
the bifid tail of the comet. Sir William Herschel found 
that the brilliant interior circular mass lost the distinct- 
ness of its outline as he increased the magnifying power 
of the telescope, and presented the appearance of a 
more and more diffuse mass of greenish or bluish-green 
light, whose intensity decreased gradually, not from the 
center, but from an eccentric brilliant speck, supposed 
to be the trtfly solid part of the comet. The luminous 
envelop was of a decided yellow, which contrasted 
strongly with the greenish tint of the interior nebulous 
mass. Stars were nearly veiled by the luminous en- 
velop, while, on the contrary, Sir William Herschel saw 
three extremely small stars shining clearly in the black 
space, which was singularly transparent. As the en- 
velop* were formed in succession as the comet ap- 
proached the sun, Sir William Herschel conceived them 
to be vapors raised by his heat at the surface of the 
nucleus, and suspended round it like a vault or dome by 
the elastic force of an extensive and highly transparent 
atmosphere. In coming to the sun, the coatings began 
to form when the comet was as distant as the orbit of 
Jupiter, and in its return they very soon entirely van- 
ished ; but a new one was formed after it had retreated 
as far as the orbit of Mars, which lasted for a few days. 
23 GG2 



354 TAILS OF COMETS. SECT. XXXVI. 

Indeed, comets in general are subject to sudden and 
violent convulsions in their interior, even when far from 
the sun, which produce changes that are visible at enor- 
mous distances, and baffle all attempts at explanation, 
probably arising from electricity, or even causes with 
which we are unacquainted. The envelops surrounding 
the nucleus of the comet on the side next to the sun, 
diverge on the opposite side, where they are prolonged 
into the form of a hollow cone, which is the tail. Two 
repulsive forces seem to be concerned in producing 
this effect ; one from the" comet and another from the 
sun, the latter being the most powerful. The envelops 
are nearer the center of the comet on the side next to 
the sun, where these forces are opposed to one an- 
other; but on the other side the forces conspire to 
form the tail, conveying the nebulous particles to enor- 
mous distances. 

" The lateral edges of the tail reflect more light than 
the central part, because the line of vision passes through 
a greater depth of nebulous matter, which produces the 
effect of two streams somewhat like the aurora. Stars 
shine with undiminished lustre through the central part 
of the tail, because their rays traverse it perpendicularly 
to its thickness ; but though distinctly seen through its 
edges, their light is weakened by its oblique transmis- 
sion. The tail of the great comet of 1811 was of won- 
derful tenuity ; stars which would have been entirely 
concealed by the slightest fog, were seen through 64,000 
leagues of nebulous matter without the smallest refrac- 
tion. Possibly some part of the changes in the appear- 
ance of the tails arises from rotation. Several comets 
have been observed to rotate about an axis passing 
through the center of the tail. That of 1825 performed 
its rotation in 20 hours, and the rapid changes in the 
luminous sectors which issued from the nucleus of Hal- 
ley's comet, in all probability were owing to rotatory 
motion. 

The two streams of light which form the edges of the 
tail, in most cases unite at a greater or less distance from 
the nucleus, and are generally situate in the plane of 
the orbit. The tails follow comets in their descent 
toward the sun, but precede them in their return, with 



S*cr. XXXVI. TAILS OF COMETS. 365 

a small degree of curvature ; their apparent extent and 
form vary according to the positions of the orbits with 
regard to the ecliptic. In some cases, the tail has been 
at right angles to the line joining the sun and comet. 
The curvature is in part owing to the resistance of the 
ether and partly to the velocity of the comet being 
greater than that of the particles at the extremity of its 
tail, which lag behind. The tails are generally of enor- 
mous lengths ; the comet of 1811 had one no less than a 
hundred millions of miles in length, and those which 
appeared in the years 1618, 1680, and 1769, had tails 
which extended respectively over 104, 90, and 97 de- 
grees of space. Consequently, when, the heads of these 
comets were set, a portion of the extremity of their tails 
was still in the zenith. Sometimes the tail is divided 
into several branches, like the comet of 1744, which had 
six, separated by dark intervals, each of them about 4 
broad, and from 30 to 44 long. They were probably 
formed by three hollow cones of the nebulous matter 
proceeding from the different envelops, and inclosing one 
another with intervals between ; the lateral edges of 
these cones would give the appearance of six streams of 
light. The tails do not attain their full magnitude till 
the comet has left the sun. When comets first appear, 
they resemble round films of vapor with little or no tail. 
As they approach the sun, they increase in brilliancy, 
and their tail in length, till they are lost in his rays ; and 
it is not till they emerge from the sun's more vivid light 
that they assume their full splendor. They then grad- 
ually decrease, their tails diminish, and they disappear 
nearly or altogether before they are beyond the sphere 
of telescopic vision. Many comets have no tails, as for 
example Encke's comet, and that discovered by M. Biela, 
both of which are small and insignificant objects. The 
comets which appeared in the years 1585, 1763, and 
1682, were also without tails, though the latter is re- 
corded to have been as bright as Jupiter. The matter 
of the tail must be extremely buoyant to precede a body 
moving with such velocity ; indeed the rapidity of its 
ascent cannot be accounted for. It has been attributed 
to that power in the sun which produces those vibrations 
of ether which constitute light : but as this theory will 



356 TAILS OF COMETS. SECT. XXXVI. 

not account for the comet of 1824, which is said to have 
had two tails, one directed toward the sun, and a very 
short one diametrically opposite to it, pur ignorance on 
this subject must be confessed. In this case the repel- 
ling power of the comet seems to have been greater than 
that of the sun. Whatever that unknown power may 
be, there are instances in which its effects are enormous, 
for immediately after the great comet of 1680 had passed 
its perihelion, its tail was 100,000,000 miles in length, 
and was projected from the comet's head in the short 
space of two days. A body of such extreme tenuity as 
a comet is most likely incapable of an attraction power- 
ful enough to recall matter sent to such an enormous 
distance ; it is therefore in all probability scattered in 
space, which may account for the rapid decrease ob- 
served in the tails of comets every time they return to 
their perihelia. Should the great comet of 1843 prove 
to be the same with that of 1668, its tail must have di- 
minished considerably. 

It. is remarkable that although the tails of comets in- 
crease in length as they approach their perihelia, there 
is reason to believe that the real diameter of the head 
contracts on coming near the sun, and expands rapidly 
on leaving him. Hevelius first observed this phenome- 
non, which Encke's comet has exhibited in a very ex- 
traordinary degree. On the 28th of October, 1828, this 
comet was about three times as far from the sun as it 
was on the 24th of December, yet at the first date its 
apparent diameter was twenty-five times greater than at 
the second, the decrease being progressive. M. Valz 
attributes the circumstance to a real condensation of vol- 
ume from the pressure of the ethereal medium, which 
increases most rapidly in density toward the surface of 
the sun, and forms an extensive atmosphere around him. 
It did not occur to M. Valz, however, that the ethereal 
fluid would penetrate the nebulous matter instead of 
compressing it. Sir John Herschel, on the contrary, 
conjectures that it may be owing to the alternate con- 
version of evaporable materials in the upper regions of 
the transparent atmosphere of comets into the states of 
visible cloud and invisible gas by the effects of heat and 
cold ; or that some of the external nebulous envelops 



SKCT. XXXVI. LIGHT OF COMETS. 357 

may come into view when the comet arrives at a darker 
part of the sky, which were overpowered by the supe- 
rior light of the sun while in his vicinity. The first of 
these hypotheses he considers to be perfectly confirmed 
by his observations on Halley's comet, made at the Cape 
of Good Hope, after its return from the sun. He thinks 
that in all probability the whole comet, except the dens- 
est part of its nucleus, vanished and was reduced to a 
transparent and invisible state during its passage at its 
perihelion, for when it first came into view after leaving 
the sun it had no tail, and its aspect was completely 
changed. A parabolic envelop soon began to appear, 
and increased so much and so rapidly that its augmenta- 
tion was visible to the eye. This increase continued till 
it became so large and so faint, that at last it vanished 
entirely, leaving only the nucleus and a tail, which it had 
again acquired, but which also vanished, so that at last 
the nucleus alone remained. Not only the tails, but the 
nebulous part of comets diminishes every time they re- 
turn to their perihelia ; after frequent returns they ought 
to lose it altogether, and present the appearance of a 
fixed nucleus : this ought to happen sooner to comets of 
short periods. M. de la Place supposes that the comet of 
1682 must be approaching rapidly to that state. Should 
the substances be altogether, or even to a great degree, 
evaporated, the comet would disappear forever. Possi- 
bly comets may have vanished from our view sooner than 
they would otherwise have done from this cause. 

If comets shine by borrowed light, they ought, in 
certain positions, to exhibit phases like the moon ; but 
no such appearance has been detected except in one 
instance, when they are said to have been observed by 
Hevelius and La Hire in the year 1682. In general, 
the light of comets is dull that of the comet of 1811 
was only equal to the tenth part of the light of the full 
moon yet some have been brilliant enough to be visible 
in full daylight, especially the comet of 1744, which was 
seen without a telescope at one o'clock in the afternoon, 
while the sun was shining. Hence it may be inferred 
that, although some comets maybe altogether diaphanous, 
others seem to possess a solid mass resembling a planet. 
But whether they shine by their own or by reflected 



358 LIGHT OF COMETS SECT. XXXVT. 

light has never been satisfactorily made out till now. 
Even if the light of a comet were polarized, it Would 
not afford a decisive test, since a body is capable of re- 
flecting light though it shines by its own. M. Arago, 
however, has with great ingenuity discovered a method 
of ascertaining this point, independent both of phases 
and polarization. 

Since the rays of light diverge from a luminous point, 
they will be scattered over a greater space as the dis- 
tance increases, so that the intensity of the light on a 
screen two feet from the object, is four times less than 
at the distance of one foot ; three feet from the object 
it is nine times less, and so on, decreasing in intensity 
as the squares of the distances increase. As a self- 
luminous surface consists of an infinite number of lumi- 
nous points, it is clear that the greater the extent of sur- 
face, the more intense will be the light; whence it may 
be concluded that the illuminating power of such a sur- 
face is proportional to its extent, and decreases inversely 
as the squares of the distances. Notwithstanding this, 
a self-luminous surface, plane or curved, viewed through 
a hole in a plate of metal, is of the same brilliancy at all 
possible distances as long as it subtends a sensible angle, 
because, as the distance increases, a greater portion 
comes into view, and as the augmentation of surface is 
as the square of the diameter of the part seen through 
the hole, it increases as the squares of the distances. 
Hence, though the number of rays from any one point 
of the surface which pass through the hole, decreases 
inversely as the squares of the distances, yet, as the 
extent of surface which comes into view increases also 
in that ratio, the brightness of the object is the same to 
the eye as long as it has a sensible diameter. For ex- 
ample Uranus is about nineteen times farther from the 
sun than we are, so that the sun, seen from that planet, 
must appear like a star with a diameter of a hundred 
seconds, and must have the same brilliancy to the inhab- 
itants that he would have to us if viewed through a 
small circular hole having a diameter of a hundred sec- 
onds. For it is obvious that light comes from every 
point of the sun's surface to Uranus, whereas a very 
small portion of his disc is visible through the hole : so 



SECT. XXXVI. NUMBER OF COMETS. 359 

that extent of surface exactly compensates distance. 
Since, then, the visibility of a self-luminous object does 
not depend upon the angle it subtends as long as it is 
of sensible magnitude, if a comet shines by its own light, 
it should retain its brilliancy as long as its diameter is of 
a sensible magnitude ; and even after it has lost an ap- 
parent diameter, it ought to be visible, like the fixed 
stars, and should only vanish in consequence of extreme 
remoteness. That, however, is far from being the case 
comets gradually become dim as their distance in- 
creases, and vanish merely from loss of light, while 
they still retain a sensible diameter, which is proved by 
observations made the evening before they disappear. 
It may therefore be concluded, that comets shine by 
reflecting the sun's light. The most brilliant comets 
have hitherto ceased to be visible when about five times 
as far from the sun as we are. Most of the comets 
that have been visible from the earth have their peri- 
helia within the orbit of Mars, because they are invisible 
when as distant as the orbit of Saturn : on that account 
there is not one on record whose perihelion is situate 
beyond the orbit of Jupiter. Indeed, the comet of 1756, 
after its last appearance, remained five whole years 
within the ellipse described by Saturn without being 
once seen. More than a hundred and forty comets 
have appeared within the earth's orbit during the last 
century that have not again been seen. If a thousand 
years be allowed as the average period of each, it may 
be computed, by the theory of probabilities, that the 
whole number which range within the earth's orbit 
must be 1400 ; but Uranus being about nineteen times 
more distant, there may be no less than 11,200,000 
comets that come within the known extent of our sys- 
tem. M. Arago makes a different estimate : he con- 
siders that, as thirty comets are known to have their 
perihelion distance within the orbit of Mercury, if it be 
assumed that comets are uniformly distributed in space, 
the number having their perihelion within the orbit of 
Uranus must be to thirty as the cube of the radius of 
the orbit of Uranus to the cube of the radius of the 
orbit of Mercury, which makes the number of comets 
amount to 3,529,470. But that number may * e doubled, 



360 ORBITS OF COMETS. SECT. XXXVI. 

if it be considered that, in consequence of daylight, fogs, 
and great southern declination, one comet out of two 
must be hid from us. According to M. Arago, more 
than seven millions of comets frequent the planetary 
orbits. 

The different degrees of velocity with which the 
planets and comets were originally propelled in space is 
the sole cause of the diversity in the form of their orbits, 
which depends only upon the mutual relation between 
the projectile force and the sun's attraction. 

When the two forces are exactly equal to one another, 
circular motion is produced ; when the ratio of the pro- 
jectile to the central force is exactly that of 1 to the 
square root of 2, the motion is parabolic ; any ratio be- 
tween these two will cause a body to move in an ellipse, 
and any ratio greater than that of 1 to the square root of 
2 will produce hyperbolic motion (N. 222). 

The celestial bodies might move in any one of these 
four curves by the law of gravitation ; but as one par- 
ticular velocity is necessary to produce either circular or 
parabolic motion, such motions can hardly be supposed to 
exist in the solar system, where the bodies are liable to 
such mutual disturbances as would infallibly change the 
ratio of the forces, and cause them to move in ellipses 
in the first case, and hyperbolas in the other. On the 
contrary, since every ratio between equality and that of 
1 to the square root of 2 will produce elliptical motion, it 
is found in the solar system in all its varieties, from that 
which is nearly circular, to such as borders on the para- 
bolic from excessive eUipticity. On this depends the 
stability of the system ; the mutual disturbances only 
cause the orbits to become more or less eccentric with- 
out changing their nature. 

For the same reason the bodies of the solar system 
might have moved in an infinite variety of hyperbolas, 
since any ratio of the forces, greater than that which 
causes parabolic motion, will make a body move in one 
of these curves. Hyperbolic motion is however very 
rare ; only two comets appear to move in orbits of that 
nature, those of 1771 and 1824 ; probably all such com- 
ets have already come to their perihelia, and conse- 
quently will never return. 



SKCT. XXXVH. FIXED STARS. 361 

The ratio of the forces which fixed the nature of the 
celestial orbits is thus easily explained ; but the circum- 
stances which determined these ratios, which caused 
some bodies to move nearly in circles and others to 
wander toward the limits of the solar attraction, and 
which made all the heavenly bodies to rotate and re- 
volve in the same direction, must have had their origin 
in the primeval state of things ; but as it pleases the 
Supreme Intelligence to employ gravitation alone in the 
maintenance of this fair system, it may be presumed to 
have presided at its creation. 



SECTION XXXVII. 

The Fixed Stars Their Numbers Estimation of their Distances and 
Magnitudes from their Light Stars that have vanished New Stars- 
Double Stars Binary and Multiple Systems Their Orbits and Periods 
Orbitual and Parallactic Motions Colors Proper Motions General 
Motions of all the Stars Clusters Nebulae Their Number and Forms 
Double and Stellar Nebulae Nebulous Stars Planetary Nebulae 
Constitution of the Nebula?, and Forces which maintain them Distribu- 
tion Meteorites Shooting Stars. 

GREAT as the number of comets appears to be, it is 
absolutely nothing when compared with the multitude of 
the fixed stars. About 2000 only are visible to the 
naked eye ; but when we view the heavens with a 
telescope, their number seems to be limited only by the 
imperfection of the instrument. In one hour Sir Wil- 
liam Herschel estimated that 50,000 stars passed through 
the field of his telescope, in a zone of the heavens 2 in 
breadth. This, however, was stated as an instance of 
extraordinary crowding ; but, on an average, the whole 
expanse of the heavens must exhibit about a hundred 
millions of fixed stars within the reach of telescopic 
vision. 

The stars are classed according to their apparent 
brightness, and the places of the most remarkable of 
those visible to the naked eye are ascertained with 
great precision, and formed into a catalogue, not only 
for the determination of geographical positions by their 
occultations, but to serve as points of reference for 
marking the places of comets and other celestial phe- 
HH 



362 DISTANCE OF THE STARS. SECT. XXXVII. 

nomena. The whole number of stars registered amounts 
to about 150,000 or 200,000. The distance of the fixed 
stars is too great to admit of their exhibiting a sensible 
disc ; but in all probability they are spherical, and must 
certainly be so if gravitation pervades all space, which it 
may be presumed to do, since Sir John Herschel has 
shown that it extends to the binary systems of stars. 
With a fine telescope the stars appear like a point of 
light ; their occultations by the moon are therefore 
instantaneous. Their twinkling arises from sudden 
changes in the refractive powers of the air, which would 
not be sensible if they had discs like the planets. Thus 
we can learn nothing of the relative distances of the 
stars from us, and from one another, by their apparent 
diameters. The annual parallax of all but a very few 
being insensible, shows we must be more than two 
hundred millions of millions of miles at least from them. 
Many of them, however, must be vastly more remote ; 
for of two stars that appear close together, one may be 
far beyond the other in the depth of space. The light 
of Sirius, according to the observations of Sir John 
Herschel, is 324 times greater than that of a star of the 
sixth magnitude ; if we suppose the two to be really of 
the same size, their distances from us must be in the 
ratio of 57-3 to 1, because light diminishes as the square 
of the distance of the luminous body increases. 

Nothing is known of the absolute magnitude of the 
fixed stars, but the quantity of light emitted by many 
of them shows that they must be much larger than the 
sun. Dr. Wollaston determined the approximate ratio* 
which the light of a wax candle bears to that of the sun, 
moon, and stars, by comparing their respective images 
reflected from small glass globes filled with mercury, 
whence a comparison was established between the 
quantities of light emitted by the celestial bodies them- 
selves. By this method he found that the light of the 
sun is about twenty millions of millions of times greater 
than that of Sirius, the brightest and one of the nearest 
of the fixed stars. Since the parallax of Sirius is about 
half a second, its distance from the earth must be 592,200 
tim es the distance of the sun from the earth ; and 
therefore Sirius, placed where the sun is, would appear 



Sxcr. XXXVII. DISAPPEARANCE OP STARS 363 

to us to be 3-7 times as large as the sun, and would give 
13-8 times more light. Many of the fixed stars must be 
infinitely larger than Sirius. 

Many stars have vanished from the heavens; the 
star 42 Virginfs seems to be of this number, having been 
missed by Sir John Herschel on the 9th of May, 1828, 
and not again found, though he frequently had occasion 
to observe that part of the heavens. Sometimes stars 
have all at once appeared, shone with a bright light, 
and vanished. Several instances of these temporary 
stars are on record ; a remarkable instance occurred in 
the year 125, which is said to have induced Hipparchus 
to form the first catalogue of stars. Another star ap- 
peared suddenly near a Aquilae in the year 389, which 
vanished, after remaining for three weeks as bright as 
Venus. On the 10th of October, 1604, a brilliant star 
burst forth in the constellation of Serpentarius, which 
continued visible for a year; and a more recent case 
occurred in the year 1670, when a new star was discov- 
ered in the head of the Swan, which, after becoming 
invisible, reappeared, and having undergone many varia- 
tions in light, vanished after two years, and has never 
since been seen. In 1572 a star was discovered in Cas- 
siopeia, which rapidly increased in brightness till it even 
surpassed that of Jupiter ; it then gradually diminished 
in splendor, and having exhibited all the variety of tints 
that indicate the changes of combustion, vanished sixteen 
months after its discovery, without altering its position. 
It is impossible to imagine anything more tremendous 
than a conflagration that could be visible at such a dis- 
tance. It is however suspected that this star may be 
periodical, and identical with the stars which appeared 
in the years 945 and 1264. There are probably many 
stars which alternately vanish and reappear among the 
innumerable multitudes that spangle the heavens ; the 
periods of several have already been pretty well ascer- 
tained. Of these the most remarkable is the star Omi- 
cron, in the constellation Cetus. It appears about twelve 
times in eleven years, and is of variable brightness, some- 
times appearing like a star of the second magnitude ; 
but it does not always attain the same lustre, nor does 
it increase or diminish by the same degrees. Accord- 



364 VARIABLE STARS. SECT. XXXVII. 

ing to Hevelius, it did not appear at all for four years. 
y Hydrae also vanishes and reappears every 494 days : 
and a very singular instance of periodicity is given by 
Sir John Herschel, in the star Algol or /3 Persei, which 
is described as retaining the size of a star of the second 
magnitude for two days and fourteen hours ; it then 
suddenly begins to diminish in splendor, and in about 
three hours and a half is reduced to the size of a star 
of the fourth magnitude ; it then begins again to increase, 
and in three hours and a half more regains its usual 
brightness, going through all these vicissitudes in two 
days, twenty hours, and forty-eight minutes, a Cassi- 
opeia? is also periodical, accomplishing its changes in 225 
days : the period of the star 34 Cygni is 18 years ; and 
Sir John Herschel has discovered very singular varia- 
tions in the star y of the constellation Argo. It is sur- 
rounded by a wonderful nebula, and from a star of little 
more than the second magnitude it suddenly increased 
between the years 1837 and 1838 to be a first-rate star 
of the first magnitude. At the latter period it was equal 
to Arcturus, and its brilliancy was then so great as to 
obliterate some of the details of the surrounding nebula. 
Afterward it decreased to the first magnitude, and then 
began to increase again. Sir John has also discovered 
that a Orionis may now be classed among the variable 
and periodic stars, a circumstance the more remarkable, 
as it is one of the conspicuous stars of our hemisphere, 
and yet its changes had never been remarked. The 
inferences Sir John draws from the phenomena of vari- 
able stars are too interesting not to be given in his own 
words. " A periodic change existing to so great an ex- 
tent in so large and brilliant a star as a Orionis, cannot 
fail to awaken attention to the subject, and to revive the 
consideration of those speculations respecting the possi- 
bility of a change in the lustre of our sun itself which 
were put forth by my father. If there really be a com- 
munity of nature between the sun and fixed stars, every 
proof that we obtain of the extensive prevalence of such 
periodical changes in those remote bodies adds to the 
probability of finding something of the kind nearer home. 
If our sun were ever intrinsically much brighter than at 
present, the mean temperature of the surface of our 



. XXXViL DOUBLE STABS. 365 

globe would of course be proportionally greater. I speak 
now not of periodical but secular changes. But the ar- 
gument is complicated with the consideration of the 
possibly imperfect transparency of the celestial spaces, 
and with the cause of that imperfect transparency which 
may be due to material non-luminous particles diffused 
irregularly in patches analogous to nebulae, but of greater 
extent to cosmical clouds in short of whose existence 
we have, I think, some indication in the singular and 
apparently capricious phenomena of temporary stars, 
and perhaps in the recent extraordinary sudden increase 
and hardly less sudden diminution of rj Argus." Mr. 
Goodricke has conjectured that the periodical changes 
in the stars may be occasioned by the revolution of some 
opaque body coming between us and the star, and ob- 
structing part of its light. Sir John Herschel is struck 
with the high degree of activity evinced by these changes 
in regions where, " but for such evidences, we might 
conclude all to be lifeless." He observes that our own 
sun requires nine times the period of Algol to perform 
a revolution on its own axis ; while on the other hand, 
the periodic time of an opaque revolving body sufficiently 
large to produce a similar temporary obscuration of the 
sun, seen from a fixed star, would be less than fourteen 
hours. 

Many thousands of stars that seem to be only brilliant 
points, when carefully examined are found to be in 
reality systems of two or more suns, sometimes revolving 
about a common center. These binary and multiple 
stars are extremely remote, requiring the most power- 
ful telescopes to show them separately. The first cat- 
alogue of double stars, in which their places and relative 
positions are determined, was accomplished by the tal- 
ents and industry of Sir William Herschel, to whom 
Astronomy is indebted for so many brilliant discoveries, 
and with whom the idea of their combination in binary 
and multiple systems originated an idea completely 
established by his own observations, and recently con- 
firmed by those of his son and other astronomers. The 
motions of revolution of many of these stars round a 
common center have been ascertained, and their periods 
determined with considerable accuracy. Some have, 



366 BINARY SYSTEMS. SECT. XXXVII. 

since their first discovery, already accomplished nearly 
a whole revolution ; and one, rj Coronae, is actually con- 
siderably advanced in its second period. These inte- 
resting systems thus present a species of sidereal chro- 
nometer, by which the chronology of the heavens will 
be marked out to future ages by epochs of their own, 
liable to no fluctuations from such planetary disturbances 
as take place in our system. 

In observing the relative position of the stars of a bi- 
nary system, the distance between them, and also the 
angle of position, that is, the angle which the meridian 
or a parallel to the equator makes with the line joining 
the two stars, are measured. The different values of 
the angle of position show whether the revolving star 
moves from east to west, or the contrary ; whether the 
motion be uniform or variable, and at what points it is 
greatest or least. The measures of the distances show 
whether the two stars approach or recede from one 
another. From these the form and nature of the orbit 
are determined. Were observations perfectly accurate, 
four values of the angle of position and of the corre- 
sponding distances at given epochs would be sufficient 
to assign the form and position of the curve described 
by the revolving star: this, however, scarcely ever 
happens. The accuracy of each result depends upon 
taking the mean of a great number of the best observa- 
tions, and eliminating error by mutual comparison. The 
distances between the stars are so minute that they can- 
not be measured with the same accuracy as the angles 
of position ; therefore, to determine the orbit of a star 
independently of the distance, it is necessary to assume 
as the most probable hypothesis, that the stars are sub- 
ject to the law of gravitation, and consequently that one 
of the two stars revolves in an ellipse about the other, 
supposed to be at rest, though not necessarily in the fo- 
cus. A curve is thus constructed graphically by means 
of the angles of position and the corresponding times of 
observation. The angular velocities of the tars are 
obtained by drawing tangents to this curve at stated in- 
tervals, whence the apparent distances, or radii vectores, 
of the revolving star become known for each angle of 
position ; because, by the laws of elliptical motion, they 



S*cr. XXXVH. BINARY SYSTEMS. 367 

are equal to the square roots of the apparent angular 
velocities. Now that the angles of position estimated 
from a given line, and the corresponding distances of the 
two stars, are known, another curve may be drawn, 
which will represent on paper the actual orbit of the 
star projected on the visible surface of the heavens ; so 
that the elliptical elements of the true orbit and its posi- 
tion in space may be determined by a combined system 
of measurements and computation. But as this orbit 
has been obtained on the hypothesis that gravitation 
prevails in these distant regions, which could not be 
known d priori, it must be compared with as many 
observations as can be obtained, to ascertain how far the 
computed ellipse agrees with the curve actually described 
by the star. 

By this process Sir John Herschel has discovered 
that several of these systems of stars are subject to the 
same laws of motion with our system of planets : he has 
determined the elements of their elliptical orbits, and 
computed the periods of their revolution. One of the 
stars of y Virginis revolves about the other hi 629 years ; 
the periodic time of a Corona? is 287 years ; that of 
Castor is 253 years; that of t Bootes is 1600 ; that of 
70 Ophiuchi is ascertained by Professor Encke to be 80 
years ; Professor Bessel has ascertained the period of 
61 Cygni to be 540 years ; and M. Savary, who has the 
merit of having first determined the elliptical elements 
of the orbit of a binary star from observation, has shown 
that the revolution of f Ursae is completed in 58 years. 
y Virginis consists of two stars of nearly the same mag- 
nitude. They were so far apart in the beginning and 
middle of the last century, that they were mentioned by 
Bradley and marked in Mayer's catalogue as two distinct 
stars. Now, they are so near to one another, that even 
with good telescopes they look like a single star some- 
what elongated. A series of observations, since the 
beginning of the present century, has enabled Sir John 
Herschel to determine the form and position of the el- 
liptical orbit of the revolving star with extraordinary 
truth. According to his computation, it must have ar- 
rived at its perihelion on the 18th of August of the year 
3 834. The actual proximity of the two stars must then 



368 ORBITS OF DOUBLE STARS. SECT. XXXVII. 

have been extreme, and the apparent angular velocity 
so great that it might have described an angle of 68 in 
a single year. Observations made at the Cape of Good 
Hope, by Sir John Herschel, as well as those of Captain 
Smyth, R. N., at home, correspond in proving an aug- 
mentation of velocity as the star was approaching its 
shortest distance from its primary. By the laws of el- 
liptical motion, the angular velocity of the revolving star 
must now gradually diminish, till it comes to its aphelion 
some 314 years hence. The satellite star of a Coronae 
attained its perihelion in 1835, and that of Castor will do 
the same some time in 1855. 

It sometimes happens that the edge of the orbit of a 
revolving star is presented to the earth, as in TT Serpen- 
tarii. Then the star seems to move in a straight line, 
and to oscillate on each side of its primary. Five ob- 
servations are requisite in this case for the determina- 
tion of its orbit, provided they be accurate. At the time 
Sir William Herschel observed the system in question, 
the two stars were distinctly separate : at present, one 
is so completely projected on the other, that M. Struve, 
with his great telescope, cannot perceive the smallest 
separation. On the contrary, the two stars of C Orionis, 
which appeared to be one in the time of Sir William 
Herschel, are now separated. Were this lib ration owing 
to parallax, it would be annual, from the revolution of the 
earth ; but as years elapse before it amounts to a sensi- 
ble quantity, it can only arise from a real orbitual motion 
seen obliquely. Among the triple stars, two of the stars of 
Cancri revolve about the third. There are also quadru- 
ple stars, and there are even assemblages of five and six 
stars, as 6 and or of Orion. It is remarked that, in gen- 
eral, the ellipses in which the revolving stars of binary 
systems move, are much more elongated than the orbits 
of the planets. Sir John Herschel, Sir James South, 
and Professor Struve of Dorpat, have increased Sir 
William Herschel's original catalogue of double stars to 
more than 6000, of which thirty or forty are known to 
form revolving or binary systems : and Mr. Dunlop has 
formed a catalogue of 253 double stars in the southern 
hemisphere. To this Sir John Herschel has added 
many ; but he has found that the southern hemisphere 



Stcr. XXXVII. PROPER MOTIONS OF THE STARS. 369 

is poorer than the northern in close double stars above 
the tenth magnitude. He observes, that if Mr. Dunlop's 
measures can be depended upon, 6 Eridani is perhaps 
the most remarkable of all the binary systems in the 
heavens. The revolution of the satellite star being at 
the rate of 10-67 per annum, it consequently must 
accomplish a revolution in a little more than thirty years. 
The motion of Mercury is more rapid than that of any- 
other planet, being at the rate of 107,000 miles an hour ; 
the perihelion velocity of the comet of 1680 was no less 
than 880,000 miles an hour ; but if the two stars of 6 
Eridani or Ursae be as remote from one another as the 
nearest fixed star is from the sun, the velocity of the 
revolving stars must exceed the powers of imagination. 
The discovery of the elliptical motion of the double stars 
excites the highest interest, since it shows that gravita- 
tion is not peculiar to our system of planets, but that 
systems of suns in the far distant regions of the uni- 
verse are also obedient to its laws. 

Besides revolutions about one another, some of the 
binary systems are carried forward in space by a motion 
common to both stars, toward some unknown point in 
the firmament. The two stars of 61 Cygni, which are 
nearly equal, and have remained at the distance of about 
15" from each other for fifty years, have changed their 
place in the heavens during that period, by 4' 23", with 
a motion which for ages must appear rectilinear : be- 
cause, even if the path be curved, so small a portion of 
it must appear a straight line to us. The single stars 
also have proper motions, yet so minute that the trans- 
lation of p Cassiopeiae, of 3"'74 annually, is the greatest 
yet observed : but the enormous distances of the stars 
make motions appear small to us which are in reality 
very great. Sir William Herschel conceived that, 
among many irregularities, the motions of the stars have 
a general tendency toward a point diametrically oppo- 
site to that occupied by the star Herculis, which he 
attributed to a motion of the solar system in the contrary 
direction. Should this really be the case, the stars, 
from the effects of perspective alone, would seem to 
diverge in the direction to which we are tending, and 
would apparently converge in the space we leave, and 
24 



370 PROPER MOTIONS OF THE STARS. SECT. XXXVII. 

there would be a regularity in these apparent motions 
which would in time be detected ; but if the solar sys- 
tem and the whole of the stars visible to us be carried 
forward in space by a motion common to all, like ships 
drifting in a current, it would be impossible for us, 
moving with the rest, to ascertain its direction. There 
can be no doubt of the progressive motion of the sun and 
stars, but sidereal astronomy is not far enough advanced 
to determine what relations these bear to one another ; 
it will however be known in the course of time from the 
orbits of the revolving stars of the binaiy systems. For 
if the solar system be in motion, some of the stellar 
orbits which, by the effects of perspective, appear to us 
to be straight lines, will, after a time, open and become 
elliptical by our change of place ; while others which 
now appear to be open will close, or open wider ; stars 
also which now occultate, or hide one another in certain 
points of their orbits, will, in time, cease to do so. The 
directions and magnitude of these changes will no doubt 
show the motion of our system, to what point it is tend- 
ing, and the velocity with which it moves. 

Among the multitudes of small stars, whether double 
or insulated, a few are found near enough to exhibit 
distinct parallactic motions, arising from the revolution 
of the earth in its orbit. Of two stars apparently in 
close approximation, one may be far behind the other in 
space. These may seem near to one another when 
viewed from the earth in one part of its orbit, but may 
separate widely when seen from the earth in another 
position, just as two terrestrial objects appear to be one 
when viewed in the same straight line, but separate as 
the observer changes his position. In this case the stars 
would not have real, but only apparent motion. One of 
them would seem to oscillate annually to and fro in a 
straight line on each side of the other a motion which 
could not be mistaken for that of a binary system, 
where one star describes an ellipse about the other, or, 
if the edge of the orbit be turned toward the earth, 
where the oscillations require years for their accom- 
plishment. 

This method of finding the distances of the fixed stars 
was proposed by Galileo, and attempted by Dr. Long 



SKCT. XXXVII. DISTANCE OF BINARY SYSTEMS. 371 

without success. Sir William Herschel afterward ap- 
plied it to some of the binary groups ; and though he 
did not find the thing he sought for, it led to the dis- 
covery of the orbitual motions of the double stars. 

Though the absolute distance of most of the stars is 
still a desideratum, a limit has been found under which, 
probably, none of them come. It was natural to sup- 
pose that in general the large stars are nearer to the 
earth than the small ones ; but there is now reason to 
believe that some stars, though by no means brilliant, 
are nearer to us than others which shine with greater 
splendor. This is inferred from the comparative ve- 
locity of their motions. All the stars have a general 
motion of translation, which tends ultimately to mix the 
stars of the different constellations, but none that we 
know of moves so rapidly as 61 Cygni; and on that 
account it is reckoned to be nearer to us than any 
other, for an object seems to move more quickly the 
nearer we are to it. This circumstance induced MM. 
Arago and Mathieu to endeavor to determine its an- 
nual parallax, that is, to ascertain what magnitude the di- 
ameter of the earth's orbit would have as seen from the 
star, and from that to compute its distance from the 
earth (N. 223). This has been accomplished with more 
accuracy by M. Bessel, who has found by observation, 
that the diameter of the earth's orbit of 190 millions of 
miles would be seen from the star under an angle of 
only one-third of a second, whence 61 Cygni must be 
592,200 times farther from the earth than the sun is, 
a distance which light, flying at the rate of 190,000 
miles in a second, would not pass over in less than 
nine years and three months. 

The apparent motion of five seconds annually which 
this star has, seems to us to be extremely small, but at that 
distance an angle of one second corresponds to twenty- 
four millions of millions of miles ; consequently the an- 
nual motion of 61 Cygni is one hundred and twenty 
millions of millions of miles, and yet, as M. Arago ob- 
serves, we call it a fixed star ! 

From the observations of Professor Henderson it ap- 
pears that Sirius, the brightest star in the heavens, has 
a parallax of less than the third of a second ; conse- 



372 DISTANCE OF BINARY SYSTEMS. SECT. XXXVIL 

quently it is at a greater distance than 61 Cygni : that 
of a Centauri amounts to a second of space, so that it is 
nearer the earth than any star that is known : whereas 
Mr. Airy has found that the parallax of a Lyra? is al- 
together inappreciable ; and as this is generally the case 
with the fixed stars, we may conclude that their dis- 
tances are beyond the hope of mensuration. 

All the ordinary methods fail when the distances are 
so enormous. An angle even of two or three seconds, 
viewed in the focus of our largest telescopes, does not 
equal the thickness of a spider's thread, which makes it 
impossible to measure such minute quantities with any 
degree of accuracy. In some cases, however, the bi- 
nary systems of stars furnish a method of estimating an 
angle of even the tenth of a second, which is thirty 
times more accurate than by any other means. From 
them the actual distances of some of the more remote 
stars will ultimately be known. 

Suppose that one star revolves about another in an 
orbit which is so obliquely seen from the earth as to 
look like an ellipse in a horizontal position, then it is 
clear that one half of the orbit will be nearer to us than 
the other half. Now, in consequence of the time which 
light takes to travel, we always see the satellite star in 
a place which it has already left. Hence when that 
star sets out from the point of its orbit which is nearest 
to us, its light will take more and more time to come to 
us in proportion as the star moves round to the most 
distant point in its orbit. On that account the star will 
appear to us to take more time in moving through that 
half of its orbit than it really does. Exactly the con- 
trary takes place in the other half: for the light will 
take less and less time to arrive at the earth in propor- 
tion as the star approaches nearer to us, and therefore 
it will seem to move through this half of its orbit in less 
time than it really does. This circumstance furnishes 
the means of finding the absolute breadth of the orbit in 
miles, and from that the true distance of the star from 
the earth. For, since the greatest and least distances 
of the satellite star from the earth differ by the breadth 
of its orbit, the time which the star takes to move from 
the nearest to the remotest point of its orbit is greater than 



SKCT. XXXVII. DISTANCE OF BINARY SYSTEMS. 373 

it ought to be, by the whole time its light takes to cross 
the orbit, and the period of moving through the other 
half is exactly as much less. Hence the difference be- 
tween the observed times of these two semi-revolutions 
of the star is equal lo twice the time thai its light em- 
ploys to cross its orbit; and as we know the velocity of 
light, the diameter of the orbit may be found in miles, 
and from that its whole dimensions. For the position of 
the orbit with regard to us is known by observation, as 
well as the place, inclination, and apparent magnitude 
of its major axis, or, which is the same thing, the angle 
under which it is seen from the earth. Since, then, 
three things are known in this great triangle, namely, 
the base or major axis of the orbit in miles, the angle 
opposite to it at the earth, and the angle it makes with 
the visual ray ; the distance of the satellite star from the 
earth may be found by the most simple of calculations. 
The merit of having first proposed this veiy ingenious 
method of finding the distances of the stars is due to M. 
Savary ; but unfortunately it is not of general application, 
as it depends upon the position of the orbit, and even 
then a long time must elapse before observation can fur- 
nish data, since the shortest period of any revolving star 
that we know of is thirty years : still the distances of a 
vast number of stars may be ultimately made out in this 
way ; and as one important discovery almost always leads 
to another, their masses may thus be weighed against 
that of the earth or sun. 

The only data employed for finding the mass of the 
earth, as compared with that of the sun, are the angular 
motion of our globe round the sun in a second of time, 
and the distance of the earth from the sun in miles (N. 
224). Now by the observations of the binary systems, 
we know the angular velocity of the small star round 
the great one ; and when we know the distance between 
the two stars in miles, it will be easy to compute how 
many miles the small star would fall through by the at- 
traction of the great one in a second of time. A compar- 
ison of this space with the space which the earth would 
descend through in a second toward the sun, will give 
the ratio of the mass of the great star to that of the sun 
or earth. 

Ii 



374 COLORS OF THE STARS. SECT. XXXVII. 

If it be considered that all the double stars appear sin- 
gle to the naked eye, and with ordinary instruments, 
and that it requires the highest powers of the very best 
telescopes to separate the greater number of them, the 
extreme beauty of the ingenuity and refraction necessary 
to draw such profound results from their motions may 
be in some degree appreciated. 

The double stars are of various hues, but they most 
frequently exhibit the contrasted colors. The large star 
is generally yellow, orange, or red ; and the small star 
blue, purple, or green. Sometimes a white star is com- 
bined with a blue or purple, and more rarely a red and 
white are united. In many cases, these appearances 
are due to the influence of contrast on our judgment of 
colors. For example, in observing a double star, where 
the large one is a full ruby red, or almost blood color, 
and the small one a fine green, the latter loses its color 
when the former is hid by the cross wires of the tele- 
scope. But there are avast number of instances where 
the colors are too strongly marked to be merely imagi- 
nary. Sir John Herschel observes in one of his papers 
in the Philosophical Transactions, as a very remarkable 
fact, that, although red stars are common enough, no 
example of a solitary blue, green, or purple one has yet 
been produced. 

The stars are scattered very irregularly over the fir- 
mament. In some places they are crowded together, in 
others thinly dispersed. A few groups more closely 
condensed form veiy beautiful objects even to the naked 
eye, of which the Pleiades and the constellation Coma 
Berenices are the most striking examples ; but the 
greater number of these clusters of stars appear to un- 
assisted vision like thin white clouds or vapor : such 
is the milky way, which, as Sir William Herschel has 
proved, derives its brightness from the diffused light of 
the myriads of stars that form it. Most of these stars 
appear to be extremely small, on account of their enor- 
mous distances ; and they are so numerous, that, ac- 
cording to his estimation, no fewer than 50,000 passed 
through the field of his telescope in the course of one 
hour in a zone 2 broad. This singular portion of the 
heavens, constituting part of our firmament, consists of 



Sscr. XXXVII. CLUSTERS OF STARS. 375 

an extensive mass of stars, whose thickness is small com- 
pared with its length and breadth ; the earth is placed 
near the point where it diverges into two branches, and 
it appears to be much more splendid in the Southern 
hemisphere than in the Northern. Sir John Herschel 
says, " The general aspect of the Southern circumpolar 
regions (including in that expression 60 or 70 of South 
polar distance) is in a high degree rich and magnificent, 
owing to the superior brilliancy and large development 
of the milky way, which, from the constellation of Orion 
to that of Antinous, is a blaze of light, strangely in- 
terrupted, however, with vacant and entirely starless 
patches, especially in Scorpio, near Alpha Centauri and 
the Cross, while to the north it fades away pale and 
dim, and is in comparison hardly traceable. I think it is 
impossible to view this splendid zone, with the astonish- 
ingly rich and evenly distributed fringe of stars of the 
3rd and 4th magnitude, which forms a broad skirt to its 
southern border like a vast curtain, without an impres- 
sion amounting almost to conviction, that the milky way 
is not a mere stratum, but annular, or at least that our 
system is placed within one of the poorer or almost 
vacant parts of its general mass, and that eccentrically, so 
as to be much nearer to the region about the Cross, than 
to that diametrically opposite to it." The cluster, of 
which our sun is a member, and which includes the 
milky way, and all the stars that adorn our sky, must be 
of enormous extent, since the sun is more than two hun- 
dred thousand times farther from the nearest of them 
than he is from the earth ; and the other stars, though 
apparently so close together, are probably separated from 
one another by distances equally great. In the intervals 
between the stars of our own system and far in the depths 
of space, many clusters of stars may be seen like white 
clouds or round comets without tails, either by unassisted 
vision or with ordinary telescopes ; but, seen with pow- 
erful instruments, Sir John Herschel describes them as 
conveying the idea of a globular space insulated in the 
heavens and filled full of stars, constituting a family or 
society apart from the rest, subject only to its own in- 
ternal laws. To attempt to count the stars in one of 
these globular clusters, he says, would be a vain task, 



376 NEBULAE. SECT, xxxvu. 

that they are not to be reckoned by hundreds : on a 
rough computation, it appears that many clusters of this 
description must contain ten or twenty thousand stars 
compacted and wedged together in a round space, 
whose area is not more than a tentiypart of that covered 
by the moon ; so that its center, where the stars are 
seen projected on each other, is one blaze of light 
(N. 225). If each of these stars be a sun, and if they 
be separated by intervals equal to that which separates 
our sun from the nearest fixed star, the distance which 
renders the whole cluster barely visible to the naked eye 
must be so great, that the existence of this splendid as- 
semblage can only be known to us by light which must 
have left it at least a thousand years ago. Occasionally 
clusters are so irregular and so undefined in their outline 
as merely to suggest the idea of a richer part of the 
heavens. These contain fewer stars than the globular 
clusters, and sometimes a red star forms a conspicuous 
object among them. Sir William Herschel regarded 
them as the rudiments of globular clusters in a less ad- 
vanced state of condensation, but tending to that form 
by their mutual attraction. 

Multitudes of nebulous spots are to be seen on the 
clear vault of heaven, which have every appearance of 
being clusters like those described, but are too distant to 
be resolved into stars by the most excellent telescopes. 
Vast numbers also appear to be matter in the highest 
possible degree of rarefaction, giving no indication what- 
ever of a stellar nature. These are in every state of 
condensation, from a vague film hardly to be discerned 
with telescopes of the highest powers, to such as seem 
to have actually arrived at a solid nucleus. This nebu- 
lous matter exists in vast abundance in space. No 
fewer than 2000 nebulae and clusters of stars were ob- 
served by Sir William Herschel, whose places have 
been computed from his observations, reduced to a com- 
mon epoch, and arranged into a catalogue in order of 
right ascension by his sister, Miss Caroline Herschel, a 
lady eminent for astronomical knowledge and discovery. 
Six or seven hundred nebulae have already been ascer- 
tained in the southern hemisphere ; of these the Ma- 
gellanic clouds are the most remarkable. The nature 



SKCT. XXXVH. NEBULA. 377 

and use of this nebulous matter, scattered over the 
heavens in such a variety of forms, is involved in the 
greatest obscurity. That it is a self-luminous, phos- 
phorescent, material substance, in a highly dilated or 
gaseous state, but gradually subsiding by the mutual 
gravitation, of its particles into stars and sidereal systems, 
is the hypothesis most generally received. And indeed 
this is the hypothesis of La Place with regard to the 
origin of the solar system, which he conceived to be 
formed by the successive condensations of a nebula, 
whose primeval rotation is still maintained in the rota- 
tion and revolution of the sun and all the bodies of the 
solar system in the same direction. Even at this day 
there is presumptive evidence in the structure and in- 
ternal heat of the earth, of its having been at one period 
in a gaseous state from intensely high temperature. 
But the only way that any real knowledge on this mys- 
terious subject can be obtained is by the determination 
of the form, place, and present state of each individual 
nebula ; and a comparison of these with future observa- 
tions will show generations to come the changes that 
may now be going on in these supposed rudiments of 
future systems. With this view, Sir John Herschel 
began in the year 1825 the arduous and pious task of 
revising his illustrious father's observations, Avhich he 
finished a short time before he sailed for the Cape of 
Good Hope, in order to disclose the mysteries of the 
southern hemisphere ; indeed, our firmament seems to 
be exhausted till farther improvements in the telescope 
shall enable astronomers to penetrate deeper into space. 
In a truly splendid paper read before the Royal Society 
on the 21st of November, 1833, he gives the places of 
2500 nebulae and clusters of stars. Of these 500 are 
neWj the rest he mentions with peculiar pleasure as 
having been most accurately determined by his father. 
This work is the more extraordinary, as from bad 
weather, fogs, twilight, and moonlight, these shadowy 
appearances are not visible, on an average, in England, 
above thirty nights in the year. 

The nebulae have great variety of forms. Vast multi- 
tudes are so faint as to be with difficulty discerned at all 
till they have been for some time in the field of the 
u2 



378 FORMS OF THE NEBULAE. SECT. XXXVII. 

telescope, or are just about to quit it. Occasionally 
they are so vague that the eye is conscious of some- 
thing, without being able to define what it is : but the 
unchangeableness of its position proves that it is a real 
object. Many present a large ill-defined surface, in 
which it is difficult to say where the center of the 
greatest brightness is. Some cling to stars like wisps of 
cloud ; others exhibit the wonderful appearance of an 
enormous flat ring seen very obliquely, with a lenticular 
vacancy in the center (N. 226). A very remarkable in- 
stance of an annular nebula is to be seen exactly half- 
way between /9 and y Lyrae. It is elliptical in the ratio 
of 4 to 5, and is sharply defined, the internal opening oc- 
cupying about half the diameter. This opening is not 
entirely dark, but filled up with a faint hazy light, aptly 
compared by Sir John Herschel to fine gauze stretched 
over a hoop (N. 227). There is a very remarkable 
nebula in Orion, in which there is some reason to believe 
that a new star has recently appeared. Two nebulae 
are described as most amazing objects : One like a 
dumb-bell or hour-glass of bright matter, surrounded by 
a thin hazy atmosphere, so as to give the whole an oval 
form, or the appearance of an oblate spheroid. This 
phenomenon bears no resemblance to any known object 
(N. 228). The other consists of a bright round nucleus, 
surrounded at a distance by a nebulous ring split through 
half its circumference, and having the split portions sep- 
arated at an angle of 45 each to the plane of the other. 
This nebula bears a strong similitude to the milky way, 
and suggested to Sir John Herschel the idea of a 
" brother system bearing a real physical resemblance 
and strong analogy of structure to our own" (N. 229). 
It appears that double nebulae are not unfrequent, ex- 
hibiting all the varieties of distance, position, and relative 
brightness with their counterparts the double stars. The 
rarity of single nebulae as large, faint, and as little con- 
densed in the center as these, makes it very improbable 
that two such bodies should be accidentally so near as 
to touch, and often in part to overlap each other, as these 
do. It is much more likely that they constitute systems ; 
and if so, it will form an interesting subject of future in- 
quiry to discover whether they possess orbitual motion. 



Sscr. XXXVII. STELLAR AND PLANETARY NEBULAE. 379 

Stellar nebulae form another class. These have a 
round or oval shape, increasing in density toward the 
center. Sometimes the matter is so rapidly condensed 
as to give the whole the appearance of a star with a blur, 
or like a candle shining through horn. In some in- 
stances the central matter is so highly and suddenly 
condensed, so vivid and sharply defined, that the nebula 
might be taken for a bright star surrounded by a thin 
atmosphere. Such are nebulous stars. The zodiacal 
light, or lenticular-shaped atmosphere of the sun, which 
may be seen extending beyond the orbits of Mercury 
and Venus soon after sunset in the months of April and 
May, is supposed to be a condensation of the ethereal 
medium by his attractive force, and seems to place our 
sun among the class of stellar nebulas. The stellar neb- 
ulae and nebulous stars assume all degrees of ellipticity. 
Not unfrequently they are long and narrow, like a 
spindle-shaped ray, with a bright nucleus in the center 
(N. 230). The last class mentioned by Sir John Her- 
schel are the planetary nebulae. These bodies have 
exactly the appearance of planets, with sensibly round 
or oval discs, sometimes sharply terminated, at other 
times hazy and ill-defined. Their surface, which is 
blue or bluish white, is equable or slightly mottled, and 
their light occasionally rivals that of the planets in vivid- 
ness. They are generally attended by minute stars, 
which give the idea of accompanying satellites. These 
nebulae are of enormous dimensions. One of them near 
v Aquarii has a sensible diameter of about 20", and 
another presents a diameter of 12". Sir John Her- 
schel has computed that, if these objects be as far from 
us as the stars, their real magnitude, on the lowest esti- 
mation, must be such as would fill the orbit of Uranus. 
He concludes that, if they be solid bodies of a solar 
nature, their intrinsic splendor must be greatly inferior 
to that of the sun, because a circular portion of the sun's 
disc, subtending an angle of 20", would give a light 
equal to that of a hundred full moons; while on the 
contrary, the objects in question are hardly, if at all, 
visible to the naked eye. From the uniformity of 
the discs of the planetary nebulae, and their want of 
apparent condensation, he presumes that they may 



380 DISTRIBUTION OF THE NEBULA. SECT. XXXVII 

be hollow shells, only emitting light from their sur- 
faces. 

The existence of every degree of ellipticity in the 
nebulae from long lenticular rays to the exact circular 
form and of every shade of central condensation from 
the slightest increase of density to apparently a solid 
nucleus may be accounted for by supposing the general 
constitutions of these nebulae to be that of oblate sphe- 
roidal masses of every degree of flatness, from the 
sphere to the disc, and of every variety in their density 
and ellipticity toward the center. It would be errone- 
ous, however, to imagine that the forms of these sys- 
tems are maintained by forces identical with those 
already described, which determine the form of a fluid 
mass in rotation ; because, if the nebulae be only clus- 
ters of separate stars, as in the greater number of cases 
there is every reason to believe them to be, no pressure 
can be propagated through them. Consequently, since 
no general rotation of such a system as one mass can 
be supposed, it may be conceived to be a quiescent form, 
comprising within its limits an indefinite multitude of 
stars, each of which may be moving in an orbit about 
the common center of the whole, in virtue of a law of 
internal gravitation resulting from the compound gravi- 
tation of all its parts. Sir John Herschel has proved 
that the existence of such a system is not inconsistent 
with the law of gravitation under certain conditions. 

The distribution of the nebulae over the heavens is 
even more irregular than that of the stars. In some 
places they are so crowded together as scarcely to allow 
one to pass through the field of the telescope before 
another appears, while in other parts hours elapse with- 
out a single nebula occurring. They are in general only 
to be seen with the very best telescopes, and are most 
abundant in a zone whose general direction is not far 
from the hour circles O h and 12 h , and which crosses the 
milky way nearly at right angles. Where that zone 
crosses the constellations Virgo, Coma Berenices, and 
the Great Bear, they are to be found in multitudes. 

Such is a brief account of the discoveries contained 
in Sir John Herschel's paper, which, for sublimity of 
views and patient investigation, has not been surpassed. 



Sscr. XXXV11. METEORITES. 381 

To him and to Sir William Herschel we owe almost all 
that is known of sidereal astronomy : and in the inimi- 
table works of that highly gifted father and son, the 
reader will find this subject treated of in a style alto- 
gether worthy of it, and of them. 

Sir John Herschel has discovered some new and 
wonderful objects in the southern hemisphere. Among 
others a beautiful planetary nebula, having a perfectly 
sharp, well defined disc of uniform brightness, exactly 
like a small planet with a satellite near its edge. Another 
is mentioned as being very extraordinary from its blue 
tint : but by far the most singular is a close double star 
centrally involve.d in a nebulous atmosphere. 

So numerous are the objects which meet our view in 
the heavens, that we cannot imagine a part of space 
where some light would not strike the eye ; innumera- 
ble stars, thousands of double and multiple systems, clus- 
ters in one blaze with their tens of thousands of stars, 
and the nebulae amazing us by the strangeness of their 
forms and the incomprehensibility of their nature, till at 
last, from the limit of our senses, even these thin and airy 
phantoms vanish in the distance. If such remote bodies 
shone by reflected light, we should be unconscious of 
their existence. Each star must then be a sun, and may 
be presumed to have its system of planets, satellites, 
and comets, like our own ; and, for aught we know, 
myriads of bodies may be wandering in space unseen 
by us, of whose nature we can form no idea, and still 
less of the part they perform in the economy of the 
universe. Even in our own system, or at its farthest 
limits, minute bodies may be revolving like the new 
planets, which are so small that their masses have hith- 
erto been inappreciable, and there may be many still 
smaller. Nor is this an unwarranted presumption ; 
many such do come within the sphere of the earth's 
attraction, are ignited by the velocity with which they 
pass through the atmosphere, and are precipitated with 
great violence on the earth. The fall of meteoric stones 
is much more frequent than is generally believed. 
Hardly a year passes without some instances occurring ; 
and if it be considered that only a small part of the earth 
is inhabited, it may be presumed that numbers fall in 



380 DISTRIBUTION OF THE NEBULAE. SECT. XXXVJI 

be hollow shells, only emitting light from their sur- 
faces. 

The existence of every degree of ellipticity in the 
nebulae from long lenticular rays to the exact circular 
form and of every shade of central condensation from 
the slightest increase of density to apparently a solid 
nucleus may be accounted for by supposing the general 
constitutions of these nebulae to be that of oblate sphe- 
roidal masses of every degree of flatness, from the 
sphere to the disc, and of every variety in their density 
and ellipticity toward the center. It would be errone- 
ous, however, to imagine that the forms of these sys- 
tems are maintained by forces identical with those 
already described, which determine the form of a fluid 
mass in rotation ; because, if the nebula? be only clus- 
ters of separate stars, as in the greater number of cases 
there is every reason to believe them to be, no pressure 
can be propagated through them. Consequently, since 
no general rotation of such a system as one mass can 
be supposed, it may be conceived to be a quiescent form, 
comprising within its limits an indefinite multitude of 
stars, each of which may be moving in an orbit about 
the common center of the whole, in virtue of a law of 
internal gravitation resulting from the compound gravi- 
tation of all its parts. Sir John Herschel has proved 
that the existence of such a system is not inconsistent 
with the law of gravitation under certain conditions. 

The distribution of the nebulae over the heavens is 
even more irregular than that of the stars. In some 
places they are so crowded together as scarcely to allow 
one to pass through the field of the telescope before 
another appears, while in other parts hours elapse with- 
out a single nebula occurring. They are in general only 
to be seen with the very best telescopes, and are most 
abundant in a zone whose general direction is not far 
from the hour circles O h and 12 h , and which crosses the 
milky way nearly at right angles. Where that zone 
crosses the constellations Virgo, Coma Berenices, and 
the Great Bear, they are to be found in multitudes. 

Such is a brief account of the discoveries contained 
in Sir John Herschel's paper, which, for sublimity of 
views and patient investigation, has not been surpassed. 



SKCT. XXXV11. METEORITES. 381 

To him and to Sir William Herschel we owe almost all 
that is known of sidereal astronomy : and in the inimi- 
table works of that highly gifted father and son, the 
reader will find this subject treated of in a style alto- 
gether worthy of it, and of them. 

Sir John Herschel has discovered some new and 
wonderful objects in the southern hemisphere. Among 
others a beautiful planetary nebula, having a perfectly 
sharp, well defined disc of uniform brightness, exactly 
like a small planet with a satellite near its edge. Another 
is mentioned as being very extraordinary from its blue 
tint : but by far the most singular is a close double star 
centrally involved in a nebulous atmosphere. 

So numerous are the objects which meet our view in 
the heavens, that we cannot imagine a part of space 
where some light would not strike the eye ; innumera- 
ble stars, thousands of double and multiple systems, cms- . 
ters in one blaze with then* tens of thousands of stars, 
and the nebulae amazing us by the strangeness of their 
forms and the incomprehensibility of their nature, till at 
last, from the limit of our senses, even these thin and airy 
phantoms vanish in the distance. If such remote bodies 
shone by reflected light, we should be unconscious of 
their existence. Each star must then be a sun, and may 
be presumed to have its system of planets, satellites, 
and comets, like our own ; and, for aught we know, 
myriads of bodies may be wandering in space unseen 
by us, of whose nature we can form no idea, and still 
less of the part they perform in the economy of the 
universe. Even in our own system, or at its farthest 
limits, minute bodies may be revolving like the new 
planets, which are so smaU that their masses have hith- 
erto been inappreciable, and there may be many still 
smaller. Nor is this an unwarranted presumption; 
many such do come within the sphere of the earth's 
attraction, are ignited by the velocity with which they 
pass through the atmosphere, and are precipitated with 
great violence on the earth. The fall of meteoric stones 
is much more frequent than is generally believed. 
Hardly a year passes without some instances occurring ; 
and if it be considered that only a small part of the earth 
is inhabited, it may be presumed that numbers fall in 



3B4 SHOOTING STARS. SKCT. XXXVII. 

By far the most extraordinary part of the whole phe- 
nomenon is that this radiant point was observed to re- 
main stationaiy near the star y Leonis for more than 
two hours and a half, which proved the source of the 
meteoric shower to be altogether independent of the 
earth's rotation, and its parallax showed it to be far 
above the atmosphere. 

As a body could not be actually at rest in that posi- 
tion, the group or nebula must either have been moving 
round the earth or the sun. Had it been moving about 
the earth, the course of the meteors would have been 
tangential to its surface, whereas they fell almost per- 
pendicularly, so that the earth in its annual revolution 
must have met with the group. The bodies or the 
parts of the nebula that were nearest must have been 
attracted toward the earth by its gravity, and as they 
were estimated to move at the rate of fourteen miles in 
a second, they must have taken fire on entering our 
atmosphere, and been consumed in their passage through 
it. 

As all the circumstances of the phenomenon were 
similar on the same day and during the same hours in 
1832, and as extraordinary flights of shooting stars were 
seen at many places both in Europe and America on 
the 13th of November, 1834, 1835, and 1836, tending 
also from a fixed point in the constellation Leo, it has 
been conjectured, with much apparent probability, that 
this nebula or group of bodies performs its revolution 
round the sun in a period of about 182 days, in an ellip- 
tical orbit, whose major axis is 119 millions of miles ; 
and that its aphelion distance, where it comes in contact 
with the earth's atmosphere, is about 95 millions of 
miles, or nearly the same with the mean distance of 
the earth from the sun. This body must have met 
with disturbances after 1799, which prevented it from 
encountering the earth for 32 years, and it may again 
deviate from its path from the same cause. 

As early as the year 1833, Professor Olmsted, of 
Yale College in the United States of America, had con- 
jectured that the phenomenon of shooting stars origi- 
nated in the zodiacal light, and his subsequent observa- 
tions, continued for three successive years, have tended 



SECT. XXXVIf. SHOOTING STARS, 385 

to confirm him in this opinion. He agrees with La 
Place in thinking that the zodiacal light is a nebulous 
body, revolving in the plane of the solar equator. In 
fact, this light stretches beyond the earth's orbit, making 
an angle of about 74 with the plane of the ecliptic, and 
according to observation, it is sometimes seen in the 
dawn, and sometimes in the twilight, like an inferior 
planet. It was seen by Professor Olmsted for several 
weeks previous to the 13th of November, in the morn- 
ing dawn, with an elongation (N. 231) of from 60 to 
90 west of the sun. It then by degrees withdrew from 
the morning sky, and appeared in the evenings imme- 
diately after twilight, rising like a pyramid through the 
constellations Capricornus and Aquarius, to an elonga- 
tion of more than 90 eastward of the sun. A change 
like this taking place annually about the 13th of Novem- 
ber, has led the Professor to believe that it is to the 
zodiacal light we are indebted for those splendid exhibi- 
tions of falling stars which take place at that season. 

The orbit already described is that which he formerly 
assigned to this nebulous or cometary body, but he is 
now of opinion that it has a period of something less 
than a year, which would not only account for the shoot- 
ing stare of the 13th of November, but would also ac- 
count for those that happen at all seasons, and for some 
very great showers of them that have taken place on 
two occasions near the end of April. In the position 
assigned to this orbit by Professor Olmsted, showers of 
shooting stars may happen in November and April. 
Since the last edition of this book a very able memoir 
has been published by M. Biot, in which that great 
philosopher shows that in his opinion also, meteoric 
showers are owing to the zodiacal light coming into pe- 
riodic contact with the atmosphere of the earth. Which 
of these conjectures may be nearest the truth time alone 
can show ; but certain it is that the recurrence of this 
phenomenon at the same season for seven successive 
years proves that it can arise from no accidental cause. 
25 KE 



3B<5 GRAVITATING FORCE. SECT. XXXVIII. 



SECTION XXXVIII. 

Diffusion of Matter through Space Gravitation Its Velocity-c Simplicity 
of its Laws Gravitation independent of the Magnitude and Distan-es of 
the Bodies Not impeded by the Intervention of any Substance Its 
Intensity invariable General Laws Recapitulation and Conclusion. 

THE known quantity of matter bears a very small pro- 
portion to the immensity of space. Large as the bodies 
are, the distances which separate them are immeasura- 
bly greater ; but as design is manifest in every part of 
creation, it is probable that if the various systems in the 
universe had been nearer to one another, their mutual 
disturbances would have been inconsistent with the har- 
mony and stability of the whole. It is clear that space 
is not pervaded by atmospheric air, since its resistance 
would, long ere this, have destroyed the velocity of the 
planets ; neither can we affirm it to be a void, since it 
seems to be replete with ether, and traversed in all di- 
rections by light, heat, gravitation, and possibly by influ- 
ences whereof we can form no idea. 

Whatever the laws may be that obtain in the more 
distant regions of creation, we are assured that one alone 
regulates the motions, not only of our own system, but 
also of the binary systems of the fixed stars ; and as 
general laws form the ultimate object of philosophical re- 
search, we cannot conclude these remarks without con- 
sidering the nature of gravitation that extraordinary 
power, whose effects we have been endeavoring to trace 
through some of their mazes. It was at one time im- 
agined that the acceleration in the moon's mean motion 
was occasioned by the , successive transmission of the 
gravitating force. It has been proved, that in order to 
produce this effect, its velocity must be about fifty mill- 
ions of times greater than that of light, which flies at 
the rate of 200,000 miles in a second. Its action, even 
at the distance of the sun, may therefore be regarded 
as instantaneous ; yet so remote are the nearest of the 
fixed stars, that it may be doubted whether the sun has 
any sensible influence on them. 

The curves in which the celestial bodies move bv th#. 



Scr. XXXV1U. GENERAL LAWS. 387 

force of gravitation are only lines of the second order. 
The attraction of spheroids, according to any other law 
of force than that of gravitation, would be raucji more 
complicated ; and as it is easy to prove that matter might 
have been moved according to an infinite variety of laws, 
it may be concluded that gravitation must have been se- 
lected by Divine Wisdom out of an infinity of others, as 
being the most simple, and that which gives the great- 
est stability to the celestial motions. 

It is a singular result of the simplicity of the laws of 
nature, which admit only of the observation and com- 
parison of ratios, that the gravitation and theory of the 
motions of the celestial bodies are independent of their 
absolute magnitudes and distances. Consequently, if all 
the bodies of the solar system, their mutual distances, 
and their velocities, were to diminish proportionally, they 
would describe curves in all respects similar to those in 
which they now move ; and the system might be suc : 
cessively reduced to the smallest sensible dimensions, 
and still exhibit the same appearances. We learn by 
experience that a very different law of attraction pre- 
vails when the particles of matter are placed within in- 
appreciable distances from each other, as in chemical 
and capillary attraction, the attraction of cohesion, and 
molecular repulsion, yet it has been shown that in all 
probability not only these, but even gravitation itself, is 
only a particular case of the still more general principle 
of electric action. 

The action of the gravitating force is not impeded by 
the intervention even of the densest substances. If the 
attraction of the sun for the center of the earth, and of 
the hemisphere diametrically opposite to him, were di- 
minished by a difficulty in penetrating the interposed 
matter, the tides would be more obviously affected. Its 
attraction is the same also, whatever the substances of 
the celestial bodies may be ; for if the action of the sun 
upon the earth differed by a millionth part from his ac- 
tion upon the moon, the difference would occasion, a 
periodical variation in the moon's parallax, whose maxi- 
mum would be the T j of a second, and also a variation in 
her longitude amounting to several seconds, a supposi- 
tion proved to be impossible, by the agreement of theory 



388 GRAVITATING FORCE. SECT. XXXVIII. 

with observation. Thus all matter is pervious to gravi- 
tation, and is equally attracted by it. 

Gravitation is a feeble force, vastly inferior to electric 
action, chemical affinity, and cohesion ; yet as far as 
human knowledge extends, the intensity of gravitation 
has never varied within the limits of the solar system ; 
nor does even analogy lead us to expect that it should : 
on the contrary, there is every reason to be assured that 
the great laws of the universe are immutable, like their 
Author. Not only the sun and planets, but the mi- 
nutest particles, in all the varieties of their attractions 
and repulsions, nay, even the imponderable matter of the 
electric, galvanic, or magnetic fluid,- are all obedient to 
permanent laws, though we may not be able in every case 
to resolve their phenomena into general principles. Nor 
can we suppose the structure of the globe alone to be 
exempt from the universal fiat, though ages may pass 
before the changes it has undergone, or that are now in 
progress, can be referred to existing causes with the 
same certainty with which the motions of the planets, 
and all their periodic and secular variations, are refera- 
ble to the law of gravitation. The traces of extreme 
antiquity perpetually occurring to the geologist give that 
information, as to the origin of things, in vain looked for 
in the other parts of the universe. They date the be- 
ginning of time with regard to our system ; since there 
is ground to believe that the formation of the earth was 
contemporaneous with that of the rest of the planets ; 
but they show that creation is the work of Him with 
whom " a thousand years are as one day, and one day 
as a thousand years." 

In the work now brought to a conclusion, it has been 
necessary to select from the whole circle of the sciences 
a few of the most obvious of those proximate links which 
connect them together, and to pass over innumerable 
cases both of evident and occult alliance. Any one 
branch traced through its ramifications would alone have 
occupied a volume ; it is hoped, nevertheless, that the 
view here given will suffice to show the extent to which 
a consideration of the reciprocal influence of even a few 
of these subjects may ultimately lead. It thus appears 
thnt the theory of dynamics, founded upon terrestrial 



Scr. XXXVIII. CONCLUSIUX. 389 

pheuomenH, is indispensable for acquiring a knowledge 
of the revolutions of the celestial bodies and their recip- 
rocal influences. The motions of the satellites are af- 
fected by the forms of their primaries, and the figures 
of -the planets themselves depend upon their rotations. 
The symmetry of their internal structure proves the 
stability of these rotatory motions, and the immutability 
of the length of the day, which furnishes an invariable 
standard of time ; and the actual size of the terrestrial 
spheroid affords the means of ascertaining the dimensions 
of the solar system, and provides an invariable founda- 
tion for a system of weights and measures. The mutual 
attraction of the celestial bodies disturbs the fluids at 
their surfaces, whence the theory of the tides and of the 
oscillations of the atmosphere. The density and elas- 
ticity of the air, varying with every alternation of tern-' 
perature, lead to the consideration of barometrical 
changes, the measurement of heights, and capillary at- 
traction ; and the doctrine of sound, including the theory 
of music, is to be referred to the small undulations of 
the aerial medium. A knowledge of the action of mat- 
ter upon light is requisite for tracing the curved path of 
its rays through the atmosphere, by which the true 
places of distant objects are determined whether in the 
heavens or on the earth. By this we learn the nature 
and properties of the sunbeam, the mode of its propaga- 
tion through the ethereal fluid, or in the interior of ma- 
terial bodies, and the origin of color. By the eclipses of 
Jupiter's satellites, the velocity of light is ascertained ; and 
that velocity, in the aberration of the fixed stars, fur- 
nishes the only direct proof of the real motion of the 
earth. The effects of the invisible rays of light are im- 
mediately connected with chemical action ; and heat, 
forming a part of the solar ray so essential to animated 
and inanimated existence, whether considered as invisi- 
ble light or as a distinct quality, is too important an agent 
in the economy of creation, not to hold a principal place 
in the connection of physical sciences. Whence follows 
its distribution in the interior and over the surface of the 
globe, its power on the geological convulsions of our 
planet, its influence on the atmosphere and on climate, 
and its effects on vegetable and animal life, evinced in 
K K 2 



390 CONCLUSION. SKCT. XXXV1U. 

the localities of organized beings on the earth, in the 
waters, and in the air. The connection of heat with 
electrical phenomena, and the electricity of the atmos- 
phere, together with all its energetic effects, its identity 
with magnetism and the phenomena of terrestrial po- 
larity, can only be understood from the theories of these 
invisible agents, and are, probably, identical with, or at 
least the principal causes of, chemical affinities. Innu- 
merable instances might be given in illustration of the 
immediate connection of the physical sciences, most of 
which are united still more closely by the common bond 
of analysis, which is daily extending its empire, and will 
ultimately embrace almost every subject in nature in its 
formulae. 

These formulae, emblematic of Omniscience, condense 
into a few symbols the immutable laws of the universe. 
This mighty instrument of human power itself originates 
in the primitive constitution of the human mind, and 
rests upon a few fundamental axioms, which have eter- 
nally existed in Him who implanted them in the breast 
of man when He created him after His own image. 



NOTE S. 



NOTE 1^ page 2. Diameter. A straight line passing through the cen- 
ter, and terminated both ways by the sides or surface of a figure, such as 
of a circle or sphere. In fig. 1, q (J, N S, are diameters. 

NOTE 2, p. 2. Mathematical and mechanical sciences. Mathematics 
leach the laws of number and quantity ; mechanics treat of the equi- 
librium and motion of bodies. 

NOTE 3, p. 2. .Analysis is a series of reasoning conducted by signs or 
symbols of the quantities whose relations form the subject of inquiry. 

NOTE 4, p. 3. Oscillations are movements to and fro, like the swing- 
ing of the pendulum of a clock, or waves in water. The tides are oscil- 
lations of the sea. 

NOTE 5, p. 3. Gravitation. Gravity is the reciprocal attraction of 
matter on matter ; gravitation is the difference between gravity and the 
centrifugal force induced by the velocity of rotation or revolution. Sen- 
sible gravity, or weight, is a particular instance of gravitation. It is the 
force which causes substances to fall to the surface of the earth, and 
which retains the celestial bodies in their orbits. Its intensity increases 
as the squares of the distance decrease. 

NOTE 6, p. 4. Particles of matter are the indefinitely small or ultimate 
atoms into which matte r is believed to be divisible. Their form is un- 
known ; but though too small to be visible, they must have magnitude.. 

NOTE 7, p. 4. J hollow sphere. A hollow ball^ like a bomb-shell. A 
sphere is a ball or solid body, such, that all lines drawn from its center 
to- its surface are equal. They are palled radii, and every line passing 
through the center and terminated both ways by the surface is a diameter, 
which is consequently equal to twice the radius. In fig. 3, Q q or N S is 
a diameter, and C Q, C N are radii. A great circle of the sphere has the 
same center with the sphere as the circles QEqd and Q. N q 3. The 
circle A B is a lesser circle of the sphere. 

NOTE 8, p. 4. Concentric hollow spheres. Shells, or hollow spheres, 
having the same center, like the coats of an onion. 

NOTE 9, p. 4. Spheroid. A solid body, which sometimes has the shape 



Fi<r. I. 







392 



AOTEri. 




of an orange, as m fig. 1 ; it is then called an oblate spheroid, because it 
is flattened at the poles N and S. Such 
is the form of the earth and planets. 
When, on the contrary, it is drawn out 
of the poles like an egg, as in fig. 2, it is 
called a prolate spheroid. It is evident 
that in both these solids the radii C g, C a, 
CN, &c., are generally unequal ; where- 
as in the sphere they are all equal. 

NOTE 10, p. 4, Center of gravity. A 
point in every body, which if supported, 
the body will remain at rest in what- 2 
ever position it may be placed. About 
that point all the parts exactly balance 
one another. The celestial bodies at- 
tract each other as if each were con- 
densed into a single particle situate in 
the center of gravity, or the particle situ- 
ate in the center of gravity of each may 
be regarded as possessing the resultant 
power of the innumerable oblique forces which constitute the whole 
attraction of the body. 

NOTE 11, pp. 4, G. Poles and equator. Let fig. 1 or 3 represent the 
earth, C its center, NCS the axis of rotation, or the imaginary line about 
which it performs its daily revolution. Then N and S are the north and 
south poles, and the great circle q E Q, which divides the earth into two 
equal parts, is the equator. The 
earth is flattened at the poles fig. 
1, the equatorial diameter, g Q, 
exceeding the polar diameter, N S, 
by about 26 miles. Lesser cir- 
cles, A B G, which are parallel to 
the equator, are circles or parallels 
of latitude, which is estimated in 
degrees, minutes, and seconds, 
north and south of the equator, 
every place in the same parallel 
having the same latitude : Green- 
wich is in the parallel of 5128'40". 
Thus terrestrial latitude is the an- 
gular distance between the direc- 
tion of a plumb-line at any place 
and the plane of the equator. 
Lines such as NClS, NGES, 
fig. 3, are called meridians ; all the places in any one of these lines have 
noon at the same instant. The meridian of Greenwich has been chosen 
by the British as the origin of terrestrial longitude, which is estimated in 
degrees, minutes, and seconds, east and west of that line. If N G E S be 
the meridian of Greenwich, the position of any place, B, is determined, 
when its latitude, Q,CB, and its longitude, EC Q, are known. 

NOTE 12, p. 4. Mean quantities are such as are intermediate between 
others that are greater and less. The mean of any number of unequal 
quantities is equal to their sum divided by their number. For instance, 
the mean between two unequal quantities'is equal to half their sum. 

NOTE 13, p. 4. Ji certain mean latitude. The attraction of a sphere on 
an external body is the same as if its mass were collected into one heavy 
particle in its center of gravity, and the intensity of its attraction dimin- 
ishes as the square of its distance from the external body increases. But 




NOTES. 



393 



the attraction of a spheroid, fig. 1, on an external body at m in the plane 
of its equator, E Q,, is greater, and its attraction on the same body when 
at m' in tiie axis X S less, than if it were a sphere. Therefore, in both 
cases, the Ibrce deviates from the exact law of gravity. This deviation 
arises from the protuberant matter at the equator ; and as it diminishes 
toward the poles, so does the attractive force of the spheroid. But there 
is one mean latitude, where the attraction of a spheroid is the same as 
if it were a sphere. It is a part of the spheroid intermediate between the 
equator and the pole. In that latitude the square of the sine is equal to 
of the equatorial radius. 

NOTE 14, p. 4. Mean distance.. The mean distance of a planet from 
the center of the sun, or of a satellite from the center of its planet, is 
equal to half the sum of its greatest and least distances, and consequently 
is equal to half the major axis of its orbit. For example, let PQ, A D, 
fig. 6, be the orbit or path of the moon or of a planet ; then P A is the 
major axis, C the center, and CS is equal to CF. Now, since the earth 
or the sun is supposed to be in the point S according as P D A Q, is regarded 
as the orbit of the moon or that of a planet, S A, S P are the greatest and 
least distances. But half the sum of S A and S P is equal to half of A P, 
the major axis of the orbit. When the body is at Q. or D, it is at its 
mean distance from S, for S <i, S D are each equal to C P, half the major 
axis by the nature of the curve. 

NOTE 15, p. 4. Mean radius of the earth. The distance from the cen- 
ter to the surface of the earth, regarded aa a sphere. It is intermediate 
between the distances of the center of the earth from the pole and from 
the equator. 

NOTE 16, p. 5. Ratio. The relation which one quantity bears to 
another. 

NOTE 17, p. 5. Square of moon's distance. In order to avoid large 
numbers, the mean radius of the earth is taken for unity : then the mean 
distance of the moon is expressed by 60 ; and the square of that number 
is 3600, or 60 tunes 60. 

NOTE 18, p. 5. Centrifugal force. The force with which a revolving 
body tends to fly from the center of motion : a sling 'tends to fly from the 
hand in consequence of the centrifugal force. A tangent is a straight line 
touching a curved line in one point without cutting it, as mT, fig. 4. The 
direction of the centrifugal force is 
in the tangent to the curved line or 
path in which the body revolves, 
and its intensity increases with the 
angular swing of the body, and with, 
its distance from the center of mo- 
tion. As the orbit of the moon does 
not differ much from a circle, let it 
be represented by m dg h, fig. 4, 
the earth being in C. The centri- 
fugal force arising from the velocity 
of the moon in her orbit balances 
the attraction of the earth. By their 
joint action, the moon moves through 
the arc m n during the time that she 
would fly off in the tangent mT by 
the action of the centrifugal force 
atone, or fall through mp by the 
earth's attraction alone. T n, the 
deflection from the tangent, is parallel and equal to mp, the versed sine 
of the arc m n, supposed to be moved over by the moon in a second, and 
therefore so very small that it may be regarded as a straight line. T w, 




394 



NOTES. 



or mp, is the space the iwoon would fall through in the first second of 
her descent to the earth, were she not retained in her orbit by her cen- 
trifugal force. 

NOTE 19, p. 5. Action and reaction. When motion is communicated 
by collision or pressure, the action of the body which strikes is returned 
with equal force by the body which receives the blow. The pressure of 
a hand on a table is resisted with an equal and contrary force. This 
necessarily follows from the impenetrability of matter, a property by which 
no two particles of matter can occupy the same identical portion of space 
at the same time. When motion is communicated without apparent 
contact, as in gravitation, attraction, and repulsion, the quantity of motion 
gained by the one body is exactly equal to that lost by the other, but in a, 
contrary direction ; a circumstance known by experience only. 

NOTE 20, p. 5. Projected. A body is projected when it is thrown ; u 
ball fired from a gun is projected ; it is therefore called a projectile. But 
the word has also another meaning. A line, surface, or solid body, is 
said to be projected upon a plane, when parallel straight lines are drawn 
from every point of it to the plane. The figure so traced upon the plane 
is a projection. The projection of a terrestrial object is therefore its day- 
light shadow, since the sun's rays are sensibly parallel. 

NOTE 21 , p. 5. Space. The boundless region which contains all creation. 

NOTE 22, pp. 5, 12. Conic Sections. Lines formed by any plane cut- 



Fig. 6. 





Fig.l. 



Fig. 8. 







NOTES. 395 

ting a cone. A cone is a solid figure, like a sugar-loaf, fig. 5, of which A 
is the apex, AD the axis, and the plane BECF the base. The axis 
may or may not be perpendicular to the base, and the base may be a 
circle, or any other curved line. When the axis is perpendicular to the 
base, the solid is a right cone. If a right cone with a circular base be cut 
at ri-jlit a'ngles to the base by a plane passing through the apex, the sec- 
tion will be a triangle. If the cone be cut through both sides by a plane 
parallel to the base, the section will be a circle. If the cone be cut slanting 
quite through both sides, the section will be an ellipse, fig. 6. If the cone 
be cut parallel to one of the sloping sides, as A B, the section will be a 
parabola, fig. 7. And if the plane cut only one side of the cone, and be not 
parallel to the other, the section will be a hyperbola, fig. 8. Thus there 
are five conic sections. 

NOTE 23, p. 5. Inverse square of distance. The attraction of one body 
for another at the distance of two miles is four times less than at the 
distance of one mile ; at three miles, it is nine times less than at one ; at 
four miles, it is sixteen times less, and so on. That is, the gravitating 
force decreases in intensity as the squares of the distance increase. 

NOTE 24, p. 5. Ellipse. One of the conic sections, fig. 6. An ellipse 
may be drawn by fixing the ends of a string to two points, S and F, in a 
sheet of paper, and then carrying the point of a pencil round in the loop 
of the string kept stretched, the length of the strkig being greater than 
the distance between the two points. The points S and F are called the 
foci, C the center, SC or CF the eccentricity, A P the major axis, QD 
the minor axis, and P S the focal distance. It is evident that the less the 
eccentricity CS, the nearer does the ellipse approach to a circle; and 
from the construction it is clear that the length of the string SmF.is 
equal to the major axis PA. If T t be a tangent to the ellipse at TO, then 
the angle TmS is equal to the angle t mF; and as this is true for every 
point in the ellipse, it follows, that in an elliptical reflecting surface, rays 
of light or sound coming from one focus S will be reflected by the surface 
to the other focus F, since the angle of incidence is equal to" the angle of 
reflection by the theories of light and sound. 

NOTE 25, p. 5. Periodic time. The time in which a planet or comet 
performs a revolution round the sun, or a satellite about its planet. 

NOTE 26, p. 5. Kepler discovered three laws in the planetary motions 
by which the principle of gravitation is established : 1st law, That the 
radii vectores of the planets and comets describe areas proportional to the 
time. Let fig. 9 be the orbit of a planet ; Fig. 9. 

then supposing the spaces or areas PSp, 
p S a, aSb, &c. equal to one another, the 
radius vector S P, which is the line joining 
the centers of the sun and planet, passes 
over these equal spaces in equal times, 
that Is, if the line S P passes to Sp in one p 
day, it wHl come to So in two days, to S b 
in three days, and so on. 2d law, That the 
orbits or paths of the planets and comets 
are conic sections, having the sun in one of 
their foci. The orbits of the planets and 
satellites are curves like fig. 6 or 9, called 
ellipses, having the sun in the focus 8. Three comets are known to 
move in ellipses, but the greater part seem to move in parabolas, fig. 7, 
having the sun in S, though it is probable that they really move in very 
long flat ellipses; others appear to move in hyperbolas, like fig. 8. The 
third law is, that the squares of the periodic times of the planets are pro- 
portional to the cubes of their mean distances from the sun. The square 
of a number is that number multiplied by itself, and the cube of a mnu 







396 NOTES. 

ber is that number twice multiplied by itself. For example, the squares 
of the numbers 2, 3, 4, &c. are 4, 9, 16, &c., but their cubes are 8, 27, 64, 
&c. Then the squares of the numbers representing the periodic times of 
two planets are to one another as the cubes of the numbers representing 
their mean distances from the sun. So that throe of these quantities 
being known, the other may be found by the rule of three. The mean 
distances are measured in miles or terrestrial radii, and the periodic times 
are estimated in years, days, and parts of a day. Kepler's laws extend to 
the satellites. 

NOTE 27, p. 5. Mass. The quantity of matter in a given bulk. It is 
proportional to the density and volume or bulk conjointly. 

NOTE 28, p. 5. Gravitation proportional to mass. But for the resist- 
ance of the air, all bodies would fall to the ground in equal times. In 
fact a hundred equal particles of matter at equal distances from the sur- 
face of the earth would fall to the ground in parallel straight lines with 
equal rapidity, and no change whatever would take place in the circum- 
stances of their descent, if 99 of them were united in one solid mass; for 
the solid mass and the single particle would touch the ground at the 
same instant, were it not for the resistance of the air. 

NOTE 29, p. 5. Primary signifies, in astronomy, the planet about which 
a satellite revolves. The earth is primary to the moon. 

NOTE 30, p. 6. Rotation. Motion round an axis, real or imaginary. 

NOTE 31, p. 7. Compression of a spheroid. The flattening at the poles. 
It is equal to the difference between the greatest and least diameters, 
divided by the greatest ; these quantities being expressed in some stand- 
ard measure, as miles. 

NOTE 32, p. 7. Satellites. Small bodies revolving about some of the 
plane'ts. The moon is a satellite to the earth. 

NOTE 33, p. 7. Nutation. A nodding motion in the earth's axis while 
in rotation, similar to that observed in the spinning of a top. It is pro- 
duced by the attraction of the sun and moon on the protuberant matter 
at the terrestrial equator. 

NOTE 34, p. l.Jlxis of Rotation. The line, real or imaginary, about 
which a body revolves. The axis of the earth's rotation is that diameter, 
or imaginary line, passing through the center and both poles. Fig. 1 being 
the earth, N S is the axis of rotation. 

NOTE 35, p. 7. Nutation of lunar orbit. The action of the bulging 
matter at the earth's equator on the moon occasions a variation in the 
inclination of the lunar orbit to the plane of the ecliptic. Suppose the 
plane Np n, fig. 13, to be the orbit of the moon, and N m n the plane of the 
ecliptic, the earth's action on the moon causes the angle pNwi to become 
less or greater than its mean state. The nutation in the lunar orbit is the 
reaction of the nutation in the earth's axis. 

NOTE 3G, p. 7 . Translated. Carried forward in space. 

NOTE 37, p. 8. Force proportional to velocity. Since a force is meas- 
ured by its effect, the motions of the bodies of the solar system among 
themselves would be the same whether the system be at rest or not. The 
real motion of a person walking the deck of a ship at sea is compounded 
of his own motion and that of the ship, yet each takes place independently 
of the other. We walk about as if the earth were at rest, though it has 
the double motion of rotation on its axis and revolution round the sun. 

NOTE 38, p. 8. Tangent, A straight line which touches a curved 
line in one point without cutting it. In fig. 4, m T is tangent to the curve 
in the point m. In a circle the tangent is at right angles to the radius C m. 

NOTE 39, p. 8. Motion in an elliptical orbit. A planet m, fig. 6, moves 
round the sun at S in an ellipse P D A Q, in consequence of two forces 



NOTES. 



397 



one urging it in the direction of the tangent mT, and another pulling it 
toward the sun in the direction mS. Its velocity, which is greatest at 
P. decreases throughout the arc to P D A to A, where it is least, and 
increases continually as it moves along the arc A Q,P till it comes to P 
again. The whole force producing the elliptical motion varies inversely 
as the square of the distance. See Note 23. 

NOTE 40, p. 8. Radii vectores. Imaginary lines joining the center of 
the sun and the center of a planet or comet, or the centers of a planet and 
its satellite. In the circle, the radii are all equal ; but in an ellipse, fig. 6, 
the radius vector SA is greater, and SP less than ail the others. The 
r;idii vectores, S Q, S D, are equal to C A or C P, half the major axis P A, 
and consequently equal to the mean distance. A planet is at its mean 
distance from the sun when in the points Q, and D. 

NOTE 41, p. 8. Equal areas in equal times. See Kepler's 1st law in 
Note -26. p. 5. 

NOTE 42, p. 8. Major Axis.. The line P A, fig. 6 or 10. 

NOTE 43, p. 9. If the planet de- J*^ Fig. 10. 

scribed a circle, S,-c. The motion of 
a planet about the eun, in a cirele 
A B P. fig. 10, whose radius C A is 
equal to the planet's mean distance 
from him, would be equable, that 
is, its velocity, or speed, would al- 
ways be the same. Whereas, if it 
moved in the ellipse A Q. P. its 
speed would be continually vary- 
ing, by Note 39 ; but its motion is 
such, that the time elapsing be- 
tween its departure from P, and its 




return to that point agaiq, would be 
the same, whether it moved in the 
circle or in the ellipse ; for these 
curves coincide in the points P & A. 

NOTE 44, p. 9. True motion. The motion of a body in its real orbit 
PDA a, fig. 10. 

NOTE 45, p. 9. -Vean motion. Equable motion in a circle P E A B, 
fig. 10, at the mean distance C P or C m, in the time that the body would 
accomplish a revolution in its elliptical orbit P D A Q,. 



NOTE 46, p. 9. The equi- 
nox. Fig. 11 represents the 
celestial sphere, and G its 
center, where the earth is sup- 
posed to be. q T Q ^= is the 
equinoctial or great circle, 
traced in the starry heavens 
by an imaginary extension of 
the plane of the terrestrial 
equator, and E T e == is the 
ecliptic, or apparent path of " 
the sun round the earth. T :=, 
the intersection of these two 
planes, is the line of the equi- 
noxes ; T is the vernal equi- 
nox, and == the autumnal. 
When the sun i.s in these 
points, the days and nights 
are equal. They are distant 
from one another by a aetni- 



Fig. 11. 




398 NOTES. 

circle, or two right angles. The points E and e are the solstices, 
where the sun is at his greatest distance from the equinoctial. 
The equinoctial is everywhere ninety degrees distant from its poles 
N and S, which are two points diametrically opposite to one another, 
where the axis of the earth's rotation, if prolonged, would meet the 
heavens. The northern celestial pole N is within 1 24' of the pole 
star. As the latitude of any place on the surface of the earth is equal to 
the height of the pole above the horizon, it is easily determined by 
observation. The ecliptic E T e ^ is also everywhere ninety degrees 
distant from its poles P and p. The angle P C N, between the poles P 
and N of the equinectial and ecliptic, is equal to the angle e C Q., called 
the obliquity of the ecliptic. 

NOTE 47, p. $. Longitude. The vernal equinox, T, fig. 11, is the 
zero point in the heavens whence celestial longitudes, or the angular 
motions of the celestial bodies, are estimated from west to east, the 
direction in which they all revolve. The vernal equinox is generally 
called the first point of Aries, though these two points have not coin- 
cided since the early ages of astronomy, about 2233 years ago, on account 
of a motion in the equinoctial points, to be explained hereafter. If S T, 
fig. 10, be the line of the equinoxes, and T the vernal equinox, the true 
longitude of a planet p is the angle T Sp, and its mean longitude is the 
angle T C m, the sun being in S. Celestial longitude is the angular 
distance of a heavenly body from the vernal equinox ; whereas terres- 
trial longitude is the angular distance of a place on the surface of the 
earth from a meridian arbitrarily chosen, as that of Greenwich. 

NOTE 48, pp. 9, 57. Equation of the center. The difference between 
T Cm and T Sp, fig. 10; that is, the difference between the true and 
mean longitudes of a planet or satellite. The true and mean places only 
coincide in the points P and A ; in every other point of the orbit, the 
true place is either before or behind the mean place. In moving from A 
through the arc A Q. P, the true place p is behind the mean place m ; 
and through the arc PDA the true place is before the mean place. At 
its maximum, the equation of the center measures C S, the eccentricity 
of the orbit, since it is the difference between the motion of a body in 
an ellipse and in a circle whose diameter AP is the major axis of the 
ellipse. 

NOTE 49, p. 9. Apsides. The points P and A, fig. 10, at the ex- 
tremities of the major axis of an orbit. P is commonly called the 
perihelion, a Greek term, signifying round the sun ; and the point A is 
called the aphelion, a Greek term, signifying at a distance from the sun. 

NOTE 50, p. Q. Ninety degrees. A circle is divided into 360 equal 
parts, or degrees ; each degree into 60 equal parts, called minutes; and 
each minute into 60 equal parts, called seconds. It is usual to write 
these quantities thus, 15 16' 10", which means fifteen degrees, sixteen 
minutes, and ten seconds. It is clear that an arc m n, fig. 4, measures 
the angle mCn; hence we may say, an arc of so many degrees, or an 
angle of so many degrees : for if there be ten degrees in the angle 
mCn, there will be ten degrees in the arc mn. It is evident that there 
are 90 in a right angle, mC d, or quadrant, since it is the fourth part 
of 3600. 

NOTE 51, p. 9. Quadratures. A celestial body is said to be in quad- 
rature when it is 90 degrees distant from the sun. For example, in fig. 
14, if d be the sun, S the earth, and P the moon, then the moon is said to 
be in quadrature when she is in either of the points Q, or D, because the 
angles dSdand DSd, which measure her apparent distance from the 
sun, are right angles. 

NOTE 52, p. 9. Eccentricity. Deviation from circular form. In fig. 
6, C S is the eccentricity of the orbit, P Q A D. Thf less C 8, the m<re 




NOTES. 399 

nearly does the orbit or ellipse approach the circular form ; and when 
CS is zero, the ellipse becomes a circle. 

NOTE 53, p. 9. Inclination of an t orbit. Let S, fig. 12, be the center 
of the sun. P N A it, the orbit jv_. jg 

of a planet moving from west 
to east in the direction N p. 
Let E N m e n be the shadow 
or projection of the orbit on 
"the plane of the ecliptic, then 3? 
N S w is the intersection of 
these two planes, for theorbif 
rises above the plane of the 
ecliptic toward Np, and sinks 
below it at N P. The angle 
p N m, which these two planes 
make with one another, is the N 

inclination of the orbit P N p A to the plane of the ecliptic. 

NOTE 54, p. 9. Latitude of a planet. The angle p S m. fig. 12, or the 
height of the planet p above the ecliptic E N m. In this case the latitude 
is north. Thus, celestial latitude is the angular distance of a celestial 
body frour the plane of the ecliptic, whereas terrestrial latitude is the 
angular distance of a place on the surface of the earth from the equator. 

NOTE 55, p. lO.J\Todes. The two points N and a, fig. 12, in which 
the orbit N A n P of a planet or comet intersects the plane of the 
ecliptic eNEw. The part N An of the orbit lies above the plane of 
the ecliptic, and the part nPN below it. The ascending node N is the 
point through which the body passes in rising above the plane of. the 
ecliptic, and the descending node n is the point in which the body sinks 
below it. The nodes of a satellite's orbit are the points in which it 
intersects the plane of the orbit of the planet. 

NOTE 56, p. 10. Distance from the sun. S p in fig. 12. If T be the 
vernal equinox, then T Sp is the longitude of the planet p, mSp is its 
latitude, and Sp its distance from the sun. When these three quantities 
are known, the place of the planet p is determined in space. 

NOTE 57, pp. 10, 58. Elements of an orbit. Of these there are seven. 
Let P N A n, fig. 12, be the elliptical orbit of a planet, C its center, S the 
sun in one of the foci, T the point of Aries, and E N e n the plane of the 
ecliptic. The elements are, the major axis A P ; the eccentricity C S ; 
the periodic time, that is, the time of a complete revolution of the body 
in its orbit; and the fourth is the longitude of the body at any given in- 
stant: for example, that at which it passes through the perihelion. P, the 
point of its orbit nearest to the sun. That instant is assumed as the origin 
of time, whence all preceding and succeeding periods are estimated. 
These four quantities are sufficient to determine the form of the orbit and 
the motion of the body in it. Three other elements are requisite for 
determining the position of the orbit in space. These are, the angle 
T S P, the longitude of the perihelion : the angle A N e, which is the 
inclination of the orbit to the plane of the ecliptic ; and lastly, the angle 
T S N, the longitude of N the ascending node. 

NOTE 58, p. 10. Whose planes, <$-c. The planes of the orbits, as 
P N A n, fig. 12, in which the planets move, are inclined or make small 
angles e N A with the plane of the ecliptic E N e n, and cut it in straight 
lines, N S n passing through S the center of the sun. 

NOTE 59, p. 12. Momentum. Force measured by the weight of a 
body and its speed, or simple velocity, conjointly. The primitive momen- 
tum of the planets is, therefore, the quantity of motion which was im- 
pressed upon them when they were first thrown into space. 

NOTK 60, p. 12. UnftfMf pfjiiV&rivm. A body is paid to be in pqnili- 



400 



NOTES. 



Let S, fig. 13, be the sun, 
Fig. 13. 



brium when it is so balanced as to remain at rest. But there are two 
kinds of equilibrium, stable and unstable. If a body balanced in stable 
equilibrium be slightly disturbed, it will endeavor to return to rest by a 
number of movements to and fro, which will continually decrease till 
they cease altogether, and then the body will be restored to its original 
state of repose. But if the equilibrium be unstable, these movements to 
and fro, or oscillations, will become greater and greater till the equili- 
brium is destroyed. 

NOTE 61, p. 13. Retrograde. Going backward, as from east to west, 
contrary to the motion of the planets. 

NOTE 62, p. 14. Parallel directions. Such as never meet, though 
prolonged ever so far: 

NOTE 63, pp. 14, 16. The whole force, be. 
Nmw the plane of the ecliptic,^ the dis- 
turbed planet moving in its orbit 7ipN, and 
d the disturbing planet. Now, d attracts the 
sun and the planet^ with different intensities 
in the directions d S, dp : the difference only 
of these forces disturbs the motion of p ; it 
is, therefore, called the disturbing force. But 
this whole disturbing force may be regarded 
as equivalent to three forces, acting in the 
directions p S, p T, and p m. The force act- 
ing in the radius vector p S, joining the cen- 
ters of the sun and planet, is called the 
radial force. It sometimes draws the dis- 
turbed planet p from the sun, and sometimes 
brings it nearer to him. The force which 
acts in the direction of the tangent, p T, 
is called the tangential force. It disturbs 
the motion of p in longitude, that is, it accel- 
erates its motion in some parts of its orbit 
and retards it 
in others, so 
that the ra- 
dius vector 
S p does not 
move over 
equal areas 

in equal times. (See Note 26.) Forexam- 
~ pie, in the position of the bodies in fig. 14, 
it is evident that, in consequence of the 
attraction of d, the planet P will have its 
motion accelerated from Q, to C, retarded 
from C to D, again accelerated from D to 
O, and, lastly, retarded from O to Q,. The 
disturbing body is here supposed to be at 
rest, and the orbit circular ; but as both 
bodies are perpetually moving with dif- 
ferent velocities in ellipses, the perturba- 
tions or changes in the motions of P are 
very numerous. Lastly, that part of the 
disturbing force which acts in the direc- 
tion of a line p m, fig. 13, at right angles 
to the plane of the orbit N pn, may be 
called the perpendicular force. It some- 
times causes the body to approach nearer, 
nnd aornptimp-- to rfredp fnrthf>r from, the 








NOTES. 



401 



plane of the ecliptic, N m n, than it would otherwise do. The action of 
the disturbing forces is admirably explained in a work on gravitation by 
Professor Airy, of Cambridge. 

NOTE 64, pp. 16, 69. Perihelion. Fig. 10, P, the point of an orbit 
nearest the sun. 

NOTE 65, p. 16. Aphelion. Fig. 10, A, the point of an orbit farthest 
from the sun. 

NOTE 66, pp. 16, ib., 17. In fig. 15 the central force is greater than the 
exact law of gravity ; therefore the curvature Ppa is greater than Pp A 
the real ellipse ; hence the planet p comes lo the point a, called the aphe- 
lion, sooner than if It moved in the orbit Pp A, which makes the line 
PSA advance to a. In fig. 16, on the contrary, the curvature P p a is 
Fig. 15. Fig. 16. 




less than in the true ellipse, so that the planet p must move through 
more than the arc Pp A, or 180, before it comes to the aphelion a, which 
causes the greater axis P S A to recede to a. 

NOTE 67, pp. 16, 17. Motion of apsides. 
Let PSA, fig. 17, be the position of the 
elliptical orbit of a planet at any time ; 
then, by the action of the disturbing 
forces, it successively takes the position 
P' S A', P" S A", &c., till by this direct 
motion it has accomplished a revolution, 
and then it begins again ; so that the 
motion is perpetual. 



NOTE 68, p. J6. Sidereal revolution. 
The consecutive return of an object to 
the same star. 



NOTE 69, p. 16. Tropical revolution. 
object to the same tropic or equinox. 

NOTE 70, p. 17. The orbit only bulges, 
&-c. In fig- 18 the effect or the varia- 
tion in the eccentricity is shown, where 
Pp A is the elliptical Orbit at any given 
instant: after a time it will take the 
form P p' A, in consequence of the 
decrease in the eccentricity CS ; then 
the form? Pp" A.Pp'" A,"&c., conse- 
cutively from the same cause, and as * 
the mHjor axis P A always retains the 
name length, the orbit approaches more 
nd more- nearly to the circular form. 
But after this has pone on for some 
thousands of years, the orbit contracts 
aeain, and become* more and more 
elliptical. 

26 L L2 




--..U-" 

K 

The consecutive return of an 

Fig. 18. 




402 



NOTES. 



NOTE 71, pp. 18, 19. The ecliptic is the apparent path of the sun in 
the heavens. See Note 46. 

NOTE 72, p. 18. This force tends to pull, <$-c. The force in question 
acting in the direction pm, fig. 13, pulls the planet p toward the plane 
N m M, or pushes it farther above it, giving the planet a tendency to move 
in an orbit above or below its undisturbed orbit N^n, which alters the 
angle p N m, and makes the node N and tbe line of nodes N n change 
their positions. 

NOTE 73, p. 18. Motion of the nodes. Let S, fig. 19, be the sun ; S N n 
the plane of the ecliptic; P the disturbing body; and p a planet moving 
in its orbit p n, of which p n is so small a part that it is represented as a 
straight line. The plane Snp of this orbit cuts the plane of the ecliptic 
in the straight line S M. Suppose the disturbing force begins to act on p 
so as to draw the planet into the arc pp' ; then, instead of moving in 
the orbit p n, it will tend to move in the orbit pp'n', whose plane cuts 
the ecliptic in the straight line S n. If the disturbing force acts again 
upon the body when at p', so as to draw it into the arcy p", the planet 
will now tend to move in the orbit p' p" n", whose plane cuts the ecliptic 
in the straight line S n". The action of the disturbing force on the 
planet when at p'', will bring the node to n'", and so on. In this man- 
ner the node goes backward through the successive points, n,n',n",n"\ 
&c., and the line of nodes S n has a perpetual retrograde motion about 




S, the center of the sun. The disturbing force has been represented as 
acting at intervals for the sake, of illustration : in nature it is continuous, 
so that the motion of the node is continuous also ; though it is sometimes 
rapid and sometimes slow, now retrograde and now direct; but on the 
whole, the motion is slowly retrograde. 

NOTE 74, p. 18. When the disturbing planet is anywhere in the line 
SN, fig. 19, or in its prolongation, it is in the same plane with the dis- 
turbed planet; and however much it may affect its motions in that 
plane, it can have no tendency to draw it out of it. But when the 
disturbing planet is in P, at right angles to the line S N, and not in the 
plane of the orbit, it has a powerful effect on the motion of the nodes : 
between these two positions there is great variety of action. 

NOTE 75, p. 19. The changes in the inclination are extremely minute 
when compared with the motion of the node, ns evidently appears front 
fig. 19, where the angles npn', n' p' n", &c. are much smaller than the 
corresponding angles n S n', S n", &c. 

NOTE 76, p. 20. Sines and cosines. Figure 4 is a circle ; n.p K the 
sine, and Cp is the cosine of an arc mn. Suppose the radius Cm to 
begin to revolve at m, in the direction mna; then at the point m the 
sign is zero, and the cosine is equal to the radius Cm. As the line C m 



i\OTES. 



403 



revolves and takes the successive positions Cn, Co, C'6, &.C., the sines* 
n p, aq, br, &LC. of the arcs 7/171, ma, mh, &c. increase, while the corres 
ponding cosines ( ' /<. C q, C r, &c. decrease, and when the revolving radius 
takes the position (.'</, ut right angles to the diameter g i, the sine be- 
comes equal to the radius Cd, and the cosine is zero. After passing the 
point (/. the contrary happens; for the sines eK, IV, &c. diminish, and 
the cosines CK, C V, &.c. go on increasing, till at g the sine is zero, and 
the cosine is equal to the radius C g. The same alternation takes place 
through the remaining parts g A, A?/, of the circle, so that a sine or cosine 
never can exceed the radius. As the rotation of the earth is invariable, 
each point of its surface passes through a complete circle, or 360 degrees, 
in twenty-four hours, at a rate of 15 degrees in an hour. Time, there- 
fore, becomes a measure of angular motion, and vice versd, the arcs of a 
circle a measure of time, since these two quantities vary simultaneously 
and equably, and as the sines and cosines of the arcs are expressed in 
terms of the time, they vary with it. Therefore, however long the time 
may be, and how often soever the radius may revolve round the circle, 
the sines and cosines never can exceed the radius ; and us the radius is as- 
sumed to be equal to unity, their values oscillate between unity and zero. 

NOTE 77, p. 21. The small eccentricities and inclinations of the plan- 
etary orbits, and the revolutions of all the bodies in the sarae direction, 
were proved by Euler, La Grange, and La Place, to be conditions neces- 
sary for the stability of the solar system. Recently, however, the peri- 
odicity of the terms of the series expressing the perturbations was sup- 
posed to be sufficient alone, but M. Poisson has shown that to be a mistake ; 
that these three conditions are requisite for the necessary convergence 
of the series, and that therefore the stability of the system depends on 
them conjointly with the periodicity of the sines and cosines of each 
term. The author is aware that this note can only be intelligible to the 
analyst, but she is desirous of correcting an error, and the more so as the 
conditions of stability afford one of the most striking instances of design 
in the original construction of our system, and of the foresight and su- 
preme wisdom of the Divine Architect. 

NOTE 78, p. 21. Resisting medium. A fluid which resists the motions 
of bodies such as atmospheric air, or the highly elastic fluid called ether, 
with which it is presumed that space is filled. 

NOTK 79, p. 22. Obliquity of the ecliptic. The angle e T q, fig. 11, be- 
tween the plane of the terrestrial equator q T Q, and the plane of the eclip 
tic E T e. The obliquity is variable. 

A'OTK 80, p. 2-2. Invariable p'ane. In the earth the equator is the ia- 



Fig. 20 




404 



NOTES. 



variable plane which nearly maintains a parallel position with regard to 
itself while revolving about the 'sun, as in fig. 20, where EQ represents 
it. The two hemispheres balance one another on each side of this plane, 
and would still do so if al! the particles of which they consist were mov- 
able among themselves, provided the earth were not disturbed by the 
action of the sun and moon, which alters the parallelism of the equator 
by the small variation called nutation, to be explained hereafter. 

NOTE 81, p. 23. If each particle, <J-c. Let P, P', P", foe., fig. 21, be 
planets moving in their orbits about the center of gravity of the system. 

Fig. 21. 




Let P S M, P' S M', &c. be portions of these orbits moved over by the radii 
vectores, S P, S P', foe., in a given time, and let p S m, p' S m' &c. be their 
shadows or projections on the invariable plane. Then, if the numbers 
which represent the masses of the planets, P, P' &c. be respectively mul- 
tiplied by the numbers representing the areas or spaces p S m, p' S ', &c. 
the sum of the whole will be greater for the invariable plane than it 
would be for any plane that could pass through S, the center of gravity 
of the system. 

NOTE 82, p. 23. The center of gravity of the solar system lies within 
the body of the sun, because his mass is much greater than the masses 
of all the planets and satellites added together. 

NOTE 83, pp. 24, 35. Conjunction. A planet is said to be in conjunc- 
tion when it has the same longitude with the sun, and in opposition 
when its longitude differs from that of the sun by 180 degrees. Thus two 
bodies are said to be in conjunction when they are seen exactly in the 
same part of the heavens, nnd in opposition when diametrically opposite 
to one another'. Mercury and Venus, which are nearer to the sun than 
the earth, are called inferior planets, while all the others, being farther 
from the sun than the earth, are said to be superior planets. Suppose 
the earth to be atE, figure 24 ; then a superior planet will be in conjunc- 
tion with the sun at C, and in opposition to him when at O. Again, 
suppose the earth to be in O, then an inferior planet will be in conjunc- 
tion when at E, and in opposition when at F. 

NOTE 84, p. 25. The periodic inequalities are computed for a given 
time ; and consequently for a given form and position of the orbits of the 
disturbed and disturbing bodies. Although the elements of the orbits 
vary so slowly that no sensible effect is produced on inequalities of a 
short period ; yet, in the course of time, the secular variations of the ele- 
ments change the forms and relative positions of the orbits so much, that 
Jupiter and Saturn, which would have come to the same relative positions 
with regard to the sun and to one another after 850 years, do not arrive 
at the same relative positions till after 918 years. 



NOTES. 405 

NOTE 85, p. 25. Conf/rvration. The relative position of the planets 
with regard to one another, to the sun, and to the plane of the ecliptic. 

NOTE 86, p. 26. In the same manner that the eccentricity of an ellipti- 
cal orLit may be increased or diminished by the action of the disturbing 
forces, so a circular orbit may acquire less or more ellipticity from the 
same cause: It is thus that the forms of the orbit of the first and second 
satellites of Jupiter oscillate between circles and ellipses differing very 
little from Circles. 

NOTE 87, p. 27. The plane of Jupiter's equator is the imaginary plane 
passing through his center at right angles to his axis of rotation ; and 
corresponds to the plane qEQe, in fig. 1. The satellites move very 
nearly in the plane of Jupiter's equator, for if J be Jupiter, fig. 22, Pp his 




axis of rotation, eQ, his equatorial diameter, which is 6000 miles longer 
than Pp, and if JO and J E be the planes of his orbit and equator seen 
edgewise, then the orbits of his four satellites seen edgewise will have 
the positions J 1, J 2, J 3, J 4. These are extremely near to one another, 
for the angle E J O is only 3 5' 30". 

NOTE 88, p. 27. In consequence of the satellites moving so nearly in 
the plane of Jupiter's equator, when seen from the earth, they appear to 
be always very nearly in a straight line, however much they may change 
their positions with regard to one another and to their primary. For 
example, on the evenings of the 3d, 4th, 5th, and 6th of January, 1835, 
the satellites had the configurations given in fig. 23, where O is Jupiter, 

Fig. 23. 
J! - Wi Ea 



3 


2. 


/. O 3- 


'h 


A ! 


3. 


2 O / 


A 


5 j 


3 /. 


O -2 


A. 


6 1 


3 


) / 


A.' 



and 1, 2. 3, 4, are the first, second, third, and fourth satellites. The satel- 
lite is supposed to be moving in a direction from the figure toward the 
point. On the sixth evening th second satellite was seen on the disc of 
the planet. 

NOTE 89, p. 28. Angular motion or velocity is the swiftness with 
which a body revolves a sling, for example ; or the speed with which 
the surface of the earth performs its daily rotation about its axis. 

NOTE 90, p. ^.Displacement of Jupiter's orbit. The action of the 
planets occasions secular variations in the position of Jupiter's orbit, J O, 
fig. 22, without affecting the plane of his equator, J E. Again, the sun 
and satellites themselves, by attracting the protul>erant matter at Jupiter's 
equator, change the position of the plane J E without affecting J O. Both 
of these cause jerturbations in the motions of the satellites. 

NOTE 91, p. 26. Precession, with regard to Jupiter, is a retrograde 
notion of the point where the lines JO, J E, intersect fig. 22, 



406 



NOTES. 



NOTE 92, p. 29. Synodic motion of a satellite. Its motion during the 
interval between two of its consecutive eclipses. 

NOTE 93, p. 29. Opposition. A body is said \n be in opposition when 
its longitude differs from that of the sun by 18(P. If S, fig. 24, be the 



Fig. 24. 




sun, and E the earth, then Jupiter is in opposition when at O, and in 
conjunction when at C. In these positions the three bodies are in the 
same straight line. 

NOTE 94, p. 29. Eclipses of the 
satellites. Let S, fig. 25, be the sun, 
J Jupiter, and a B b his shadow. Let 
the earth be moving in its orbit, 
in the direction EARTH, and the 
third satellite in the direction abmn. 
When the earth is at E, the satellite, 
in moving through the arc a b, will 
vanish at a, and reappear at b, on the 
same side of Jupiter. If the earth be 
in R, Jupiter will be in opposition; 
and then the satellite, in moving 
through the arc a b, will vanish close 
to the disc of the planet, and will re- 
appear on the other side of it. But if 
the satellite be moving through the 
arc m n, it will appear to pass over 
the disc and eclipse the planet. 

NOTE 95, pp. 30, 42. Meridian. A 
terrestrial meridian is a line passing 
round the earth and through both 
poles. In every part of it noon hap- 
pens at the same instant. In figures 
1 and 3, the lines N Q S and N G S 
are meridians, C being the center of 
the earth, and N S its axis of rotation. 
The meridian passing through the 
Observatory at Greenwich is assumed , 
by the British as a fixed origin from / 
whence terrestrial longitudes are mea- i1 ,' 
eured. And as each point on the sur- 
face of the earth passes through 300, 
or a complete circle in twenty-four 




NOTES. 407 

Aours, at the rate of 15 degrees in an hour, time becomes a representative 
of angular motion. Hence if the eclipse of a satellite happens at any 
place at eight o'clock in the evening, and the Nautical Almanac shows 
that the same phenomenon will take place at Greenwich at nine, the 
place of observation will be in the 15 of west longitude. 

NOTE 96, p. 30. Conjunction. Let S be the sun, fig. 24, E the earth, 
and J OJ' C' the orbit of Jupiter. Then the eclipses which happen when 
Jupiter is in O are seen 16m 26 sooner than those which take place when 
the planet is inC. Jupiter is in conjunction when at C and in opposition 
when in O. 

NOTE 97, p. 30. In the diagonal, Src. Were the line A S, fig. 26, 
100,000 times longerthan^ A B, Jupiter's true place Fig. 26. 

would be in the direction A S', the diagonal of the , 

figure A B S' S, which is, of course, out of propor- 
tion. 

NOTE 98, p. 31. Aberration of light. The ce- 
lestial bodies are so distant, that the rays of light 
coming from them may be reckoned parallel. 
Therefore, let S A, S' B, fig. 26, be two rays of light 
coming from the sun, or a planet, to the earth 
moving in its orbit in the direction A B. If a tele- 
scope be held in the direction A S, the ray S A, 
instead of going down the tube, will impinge on its 
side, and be lost in consequence of the telescope 
being carried with the earth in the direction A B. 
But if the tube be held in the position A E, so that 
A B is to A S as the velocity of the earth to the 

velocity of light, the ray will pass through S' E A. 

The star appears to be in the direction A S, when 

it really is in the direction A S', hence the angle S A S' is the angle of 

aberration.. 

NOTE 99, p. 31. Density proportional to elasticity. The more a fluid, 
such as atmospheric air, is reduced in dimensions by pressure, the more 
it resists the pressure. 

NOTE 100, p. 32. Oseillation of pendulum retarded. If a clock be 
carried from the pole to the equator, its rate will be gradually diminished, 
that is, it will go slower and slower, because the centrifugal force which 
increases from the pole to the-equator, diminishes the force of gravity. 

NOTE 101, p. 33. Disturbing action. The disturbing force acts here 
in the very same manner as in note 63 ; only that the disturbing body d, 
fig. 14, is the sun, S the earth, and p the moon. 

NOTE 102. pp. 34, 36, 81. Perigee. A Greek word signifying round 
the earth. The perigee of the lunar orbit is the point P, fig. 6, where the 
moon i nearest to the earth. It corresponds to the perihelion of a planet. 
Sometimes the word is used to denote the point where the sun is nearest 
to the earth. 

NOTE 103, p. 34. Eveetion. The evection is produced by the action of 
the radial force in the direction S p, fig. 14, which sometimes increases 
and sometimes diminishes the earth's attraction to the moon. It produces 
a corresponding temporary change in the eccentricity, which varies with 
the position of the major axis of the lunar orbit in respect of the line S d, 
joining the centers of the earth and sun. 

NOTE 104, p. 34. Variation. The lunar perturbation called the varia- 
tion is the alternate acceleration and retardation of the moon in longitude, 
from the action of the tangentlnl force. She is accelerated in going from 
quadratures in Q and D, fig. 14, to the points C and O, called syzygies, 
BJid i retarded in going from the syzygies C and O to Q and D again. 



408 



NOTES. 



NOTE 105, p. 36. Square of time. If the times increase at tlie rate of 
1, 2, 3, 4, &c., years or hundreds of years, the squares of the times will 
be 1, 4, 9, 16, &c., years or hundreds of years. 

NOTE 106, p. 37. Mean anomaly. The mean anomaly of a planet is 
its angular distance from the perihelion, supposing it to move in a circle. 
The true anomaly is its angular distance from the perihelion in its ellip- 
tical orbit. For example, in fig. 10, the mean anomaly is PC m, and the 
true anomaly is P S p. 

NOTE 107, pp. 38, 63. Many circumferences. There are 360 degrees, 
or 1,296,000 seconds, in a circumference ; and as the acceleration of the 
moon only increases at the rate of eleven seconds in a century, if. must 
be a prodigious number of ages before it accumulates to many circum- 
ferences. 

NOTE 108, p. 38. Phases of the moon. The periodical changes in the 
enlightened part of her disc from a crescent to a circle, depending upon 
her position with regard to the sun and earlh. 

NOTE 109, p. 39. Lunar eclipse. Let S, fig. 27, be the sun, E the 
earth, and m the moon. The space a A b is a section of. the shadow, 

Fig. 27. 




- d 



which has the form of a cone or sugar-loaf, and the spaces A a c, A b d, 
are the penumbra. The axis of the cone passes through A, and through 
E and S, the centers of the sun and earth, and n m n' is the path of the 
moon through the shadow. 

NOTE 110 r p. 39. Apparent diameter. The diameter of a celestial body 
as seen from the earth. 

NOTE 111, p. 39. Penumbra. The shadow, or imperfect darkness, 
which precedes and follows an eclipse. 

NOTE 112, p. 39.- -Synodic revolution of the moon. The time between 
two consecutive now or full moons. 

NOTE 113, p. 39. Horizontal refraction. The light, in coming from a 
celesiial object, is ben. into a curve as soon as it enters our atmosphere, 
and that bending is greatest when the object is in the horizon. 

NOTE 114, p. 40. Solar eclipse. Let S, fig. 28, be the sun, m the moon, 
and E the earth. Then a E b is the moon's shadow, which sometimes 



Fig. 28. 




NOTES. 



409 



eclipses a small portion of the earth's surface at e, and sometimes falls 
short of it. To a person at e, in the center of the shadow, the eclipse 
may be total or annular; to a person not in the center of the shadow, a 
part of the sun will be eclipsed ; and to one at the edge of the shadow 
there will be no eclipse at all. The spaces P b E, P' a E are the pen- 
umbra. 

Fisr. 29. 



NOTE 115, p. 42. From the extremities, <J-c. 
If the length of the line a b, fig. 29, be meas- 
ured, in feet or fathoms, the angles S b a, 
Sab, can be measured, and then the angle 
oS b is known, whence the length of the line 
S C may be computed, a S b is the parallax 
of the object S, and it is clear that the greater 
the distance of 8, the less the base a b will 
appear, because the angle a S' b is less than 
a 3 ft. 



NOTE 116, p. 43. Every particle will describe a circle, Src. If N S, fig. 
3, be the axis about which the body revolves, then particles at B, Q, 
&c., will whirl in the circles B G A a, <J E qd, whose centers are in the 
axis N S, and their planes parallel to one another. They are, in fact, 
parallels of latitude, Q. E q d being the equator. 

NOTK 117, p. 43. The force of gravity, &c. Gravity at the equator 
acts in the direction d C, fig. 30 ; whereas the direction of the centrifugal 
Fiff.30. 




MM 



410 NOTES. 

force is exactly contrary, being in the direction C Q, ; hence, the differ- 
ence of the two is the force called gravitation, which makes bodies fall 
to the surface of the earth. At any point, m, not at the equator, the 
direction of gravity is m b, perpendicular to the surface ; but the centri- 
fugal force acts perpendicularly to N S, the axis of rotation. Now the 
effect of the centrifugal force is the same as if it were two forces, one of 
which, acting in the direction b m, diminishes the force of gravity ; and 
another which, acting in the direction m t, tangent to the surface at m, 
urges the particles toward Q, and tends to swell out the earth at the 
equator. 

NOTE 118, p. 44. Homogeneous mass. A quantity of matter, every- 
where of the same density. 

NOTE 119, p. 44. Ellipsoid of revolution. A solid formed by the revo- 
lution of an ellipse about its axis. If the ellipse revolve about its minor 
axis Q, D, fig. 6, the ellipsoid will be oblate, or flattened at the poles like 
an orange. If the revolution be about the greater axis A P, the ellipsoid 
will be prolate, like an egg. 

NOTE 120, p. 44. Concentric elliptical strata. Strata, or layers, having 
an elliptical form and the same center. 

NOTE 121, p. 45. On the whole, be. The line N Q S q, fig. 1, repre- 
sents the ellipse in question, its major axis being Q, q. its minor axis N S. 

NOTE 122, p. 45. Increase in the length of the radii, Src. The radii 
gradually increase from the polar radius C N, fig. 30, which is least, to 
the equatorial radius C Q., which is greatest. There is also an increase 
in the lengths of the arcs corresponding to the same number of degrees 
from the equator to the poles, for the angle N C r, being equal to q Cd, 
the elliptical arc N r is less than q d. 

NOTE 123, pp. 45, 259. Cosine of latitude. The angles mCa,mCb, fig. 
4, being the latitudes of the points a, b, &c., the cosines are C q, C r, &c. 

NOTE 124, p. 46. An arc of the meridian. Let N Q S g, fig. 30, be the 
meridian, and m n the arc to be measured. Then if Z' m, Z n, be verti- 
cals, or lines perpendicular to the surface of the earth, at the extremities 
of the arc m n they will meet in p. Q,an,Q,b m, are the latitudes of the 
points m and n, and their difference is the angle mpn. Since the lati- 
tudes are equal to the height of the pole of the equinoctial above the 
horizon of the places m and ?t, the angle mpn may be found by observa- 
tion. When the distance m n is measured in feet or fathoms, and divided 
by the number of degrees and parts of a degree contained in the angle 
mpn, the length of an arc of one degree is obtained. 

NOTE 125, p. 46. Ji scries of triangles. Let M M', fig. 31, be the 



Fig.M. 




meridian of any place. A line, A B, is measured with rods, on level 
ground, of any number of fathoms, C being some point seen from both 
ends of it. As two of the angles of the triangle ABC can be measured, 
the lengths of the sides A C, B C, can be computed ; and if the angle 
m A B, which the base A B makes with the meridian, be measured, the 
length of the sides B m, A /, may be obtained by computation, so that 



NOTES. 



411 



A , a small part of the meridian, is determined. Again, if D be a point 
visible from the extremities of the known line BC, two of the angles of 
the triangle BCD may be measured, and the length of the sides CD, 
BD, computed. Then if the angle Emm' he measured, all the angles 
and the side B m of the triangle Emm' are known, whence the length of 
the line m m' may lie computed, so that the portion A m' of the meridian 
is determined, and in the same manner it may be prolonged indefinitely. 

NOTE 126, pp. 47. 48. The square of the sine of the latitude. Q. b m, fig. 
30. being the latitude ofm,em is the sine, and b e the cosine. Then the 
number expressing the length of em, multiplied by itself, is the square of 
the sine of the latitude ; and the number expressing the length of A , 
multiplied by itself, is the square of the cosine of the latitude. 

NOTE 127, p. 49. A pendulum is that part of a clock which swings to 
and fro. 

NOTK 128, p. 51. Parallax. The angle aSft, fig. 29, under which we 
view an object a b : it therefore diminishes as the distance increases. The 
parallax of a celestial object is the angle which the radius of the earth 
would lie seen under, if viewed from that object. Let E, fig. 32, be the 



Fig. 32. 




center of the earth. E H .ts radius, and m H O the horizon of an observer 
at H. Then H m E is the parallax of a body m, the moon for example. 
As TO rises higher and higher in the heavens to the points m', m", &c., 
the parallax H m' E, H m" E, &c. decreases. At Z, the zenith, or point 
immediately above the head of the observer, it is zero; and at m, where 
the body is in the horizon, the angle H m E is the greatest possible, and 
is called the horizontal parallax. It is clear that with regard to celestial 
bodies the whole effect of parallax is in the vertical, or in the direction 
m m' Z ; and as a person at H sees m' in the direction H m' A, when it 
really is in the direction E m' B, it makes celestial objects appear to be 
lower than they really are. The distance of the moon from the earth 
has been determined from her horizontal parallax. The angle E m H 
can be measured. EH m is a right angle, and EH, the radius of the 
earth, is known in miles ; whence the distance of the moon E m is easily 
found. Annual parallax is the angle under which the diameter of the 
earth's orbit would be seen, if viewed from a star. 

NOTE 129, p. 52. The radii n B, n G, &c., fig. 3, are equal in any one 



412 NOTES. 

parallel of latitude, A a, B G ; therefore a change in the parallax ob- 
served in that parallel can only arise from a change in the moon's 
distance from the earth : and when tlie moon is at her mean distance, 
which is a constant quantity equal to half the major axis of her orbit, a 
change in the parallax observed in different latitudes, G and E, must 
arise from the difference in the lengths of the radii n G and C E. 

NOTE 130, p. 52. When Venus is in her nodes. She must be in the 
line N S n, where her orbit P N A n cute the plane of the ecliptic E N e n, 
fig. 12. 

NOTE 131, p. 52. -The line described, $rc. Let E, fig. 33, be the earth, 




S the center of the sun, and V the planet Venus. The real transit of 
the planet, seen from E the center of the earth, would be in the direction 
A B. A person at W would see it pass over the sun in the line a, and 
a person at O would see it move across him in the direction v' a'. 

NOTE 132, p. 53. Kepler's law. Suppose it were required to find the 
distance of Jupiter from the sun. The periodic times of Jupiter and 
Venus are given by observation, and the mean distance of Venus from 
the center of the sun is known in miles or terrestrial radii ; therefore, by 
the rule of three, the square root of the periodic time of Venus is to the 
square root of the periodic time of Jupiter, as the cube root of the mean 
distance of Venus from the sun, to the cube root of the mean distance of 
Jupiter from the sun, which is thus obtained in miles or terrestrial radii. 
The root of a number is that number which, once multiplied by itself, 
gives its square; twice multiplied by itself, gives its cube, &c. For 
example, twice 2 are 4, and twice 4 are 8 ; 2 is therefore the square root 
of 4, and the cube root of 8. In the same manner 3 times 3 are 9, and 3 
times 9 are 27 ; Sis therefore the square root of 9, and the cube root of 27. 

NOTE 133, p. 55. Inversely, <$-c. The quantities of matter in any two 
primary planets are greater in proportion as the cubes of the numbers 
representing the mean distances of their satellites are greater, and also in 
proportion as the squares of their periodic times are less. 

NOTE 134, p. 55. As hardly anything appears more impossible than 
that man should have been able to weigh the sun as it were in scales 
and the earth in a balance, the method of doing PO may have some 
interest. The attraction of the sun is to the attraction of the earth, as 
the quantity of matter in the sun to the quantity of matter in the earth : 
and as the force of this reciprocal attraction is measured by its effects, 
the space the earth would fall through in a second by the sun's attrac- 
tion, is to the space which the sun would fall through by the earth's 
attraction, as the mass of the sun to the mass of the earth. Hence, as 
many times as the fall of the earth to the sun in a second exceeds the 
fall of the sun to the earth in the same time, so many times does the 
mass of the sun exceed the mass of the earth. Thus the weight of the 
sun will be known if the length of these two spaces can be found in 
miles or parts of R mile. Nothing can be easier. A heavy body falls 
through 16-0697 feet in a second at the surface of the earth by the 
earth's attraction ; and as the force of gravity is inversely as the square 



NOTES. 413 

of the distance, it is clear that 16-0697 feet are to the space a body would 
fall through :it the distance of the sun by the earth's attraction, as the 
square nf tlie distance of the sun from the earth to the square of the 
distance of the center of the earth from its surface ; that is, as the square 
<>t'i.i.(KM),OOU miles to the square of 4000 miles. And thus, by a simple 
question in the rule of three, the space which the sun would fall through 
in a second by the attraction of the earth may be found in parts of a 
mile. The space the earth would fall through in a second by the attrac- 
tioa of the sun must now be found in miles also. Suppose m x, fig. 4, to 
be the arc which the earth describes round the sun in C in a second of 
time, by the joint action of the sun and the centrifugal force. By the 
centrifugal force alone the earth would move from m to T in a second, 
and by the sun's attraction alone it would fall through T n in the same 
time. Hence the length of T n in miles is the space the earth would fall 
through in a second by the sun's attraction. Now as the earth's orbit is 
very nearly a circle, if 360 degrees be divided by the number of seconds 
in a sidereal year of 365$ days, it will give mn, the arc which the earth 
moves through in a second, and then the tables will give the length of 
the line TC in numbers corresponding to that angle; but as the radius 
C it is assumed to be unity in the tables, if 1 be subtracted from the 
number representing CT, the length of Tre wHl be obtained ; and when 
multiplied by 95,000,000 to reduce it to miles, the space which the earth 
falls through by the sun's attraction will be obtained in miles. By this 
simple process it is found that if the sun were placed in one scale of a 
balance, it would require 354,936 earths to form a counterpoise. 

XOTE 135, p. 58. The sum of the greatest and least distances, S P, S A, 
fis. 1-2, is equal to PA, the major axis; and their difference is equal to 
twice the eccentricity CS. The longitude T S P of the planet, when in 
the point P, at its least distance from the sun, is the longitude of the peri- 
helion. The greatest height of the planet above the plane of the ecliptic 
E N e n is equal to the inclination of the orbit P N A n to that plane. The 
longitude of the -planet, when in the plane of the ecliptic, can only be the 
longitude of one of the points N or n ; and when one of these points is 
known, the other is given, being 180 distant from it. Lastly, the time 
included between two consecutive passages of the planet through the 
same node N or n is its periodic time, allowance being made for the recess 
of the node in the interval. 

NOTE 136, p. 59. Suppose that it were required to find the position of 
a point in space, as of a planet, and that one observation places it in n, 
fig. 34. another observation places it in n', Fig. 34. 

another hi n", and so on ; all the points 
n, ;t', n", n'", &c. being very near to one 
another. The true place of the planet P 
will not differ much from any of these 
positions. It is evident, from this view of 
the subject, that P n, P ', P n", &c. are 
the errors of observation. The true posi- 
tion of the planet P is found by this prop- 
erty, that the squares of the numbers 
representing the lines P n, P n', &.C., when, v ., 
added together, are the least possible. 
Each line P n, P n', &c. being the whole error in the place of the planet, is 
made up of the errors of all the elements; and when compared with the 
errors obtained from theory, it affords the means of finding each. The 
principle of least squares is of very general application ; its demonstration 
cannot find a place here ; but the reader is referred to Biot's Astronomy, 
vol. ii. p. 203. 

NOTE 137, p. 61. An axis that, Sre. Fig. 20 represents the earth 

M :i a 





414 NOTES. 

revolving in its orbit about the sun S, the axis of rotation Pp being every- 
where parallel to itself. 

NOTE 138, p. 61. Angular velocities that are sensibly uniform. The 
earth and planets revolve about their axes with an equable motion, which 
is never either faster or slower. For example, the length of the day is 
never more nor less than twenty-four hours. 

NOTE 139, p. 64. If fig. 1 be the moon, her polar diameter NS is the 
shortest; and of those in the plane of the equator, Q,Ey, that which 
points to the earth is greater than all the others. 

NOTE 140, p. 69. Inversely proportional, &,-c. That is, the total amount 
of solar radiation becomes less as the minor axis C C', fig. 20, of the earth's 
orbit becomes greater. 

NOTE 141, p. 70. Fig. 35 represents the 
position of the apparent orbit of the sun 
as it is at present, the earth being in E. 
The sun is nearer to the earth in moving 
through =^=P T, than in moving through 
T A:=, but its motion through =^P T 
is more rapid than its motion through 
T A ^= ; and as the swiftness of the mo- 
tion and the quantity of heat received 
vary in the same proportion, a compensa- 
tion takes place. 

NOTE 142, p. 71. In an ellipsoid of revolution, fig. 1, the polar diameter 
NS and every diameter in the equator qlS>Q,e are permanent axes of 
rotation, but the rotation would be unstable about any other. Were the 
earth to begin to rotate about C a, the angular distance from a to the equa- 
tor at q would no longer be ninety degrees, which would be immediately 
detected^ by the change it would occasion in the latitudes. 

NOTE 143, pp. 50, 75. Let q T Q,, and E T e, fig. 1 1, be the planes of the 
equator and ecliptic. The angle e If Q,, which separates them, called the 
obliquity of the ecliptic, varies in consequence of the action of the sun 
and moon upon the protuberant matter at the earth's equator. That 
action brings the point Q toward e, and tends to make the plane q T a 
coincide with the ecliptic E T e, which causes the equinoctial points, T 
and =:, to move slowly backward on the plane e T E at the rate of 50"'4l 
annually. This part of the motion, which depends upon the form of the 
earth, is called luni-solar precession. Another part, totally independent 
of the form of the earth, arises from the mutual action of the earth, 
planets, and sun, which, altering the position of the plane of the ecliptic 
e T E, causes the equinoctial points T and := to advance at the rate of 
0"-31 annually ; but as this motion is much less than the former, the 
equinoctial points recede on the plane of the ecliptic at the rate of 50"'l 
annually. This motion is called the precession of the equinoxes. 

NOTE 144, pp. 61,